Small-string final non-appearance coincidences in base-ten powers of two

If we look at OEIS A094776, one sees the beginnings of sequences that apply the inherent concept to strings of more than one digit. Keith Lynch suggested the idea (tongue-in-cheek, I thought) on MathFun a few days ago and Maximilian Hasler actually worked out the numbers for strings 10 to 18. I decided to chart a more comprehensive listing...

My results: sorted by strings and sorted by powers of two. There are "coincidences" where two or more strings share the same power of two as their final non-appearance exponent (for example, the two 71s in A094776 for digits 5 and 7). I'll list those here after brief summaries of each n-digit result:

1-digit strings

{71,5}
{71,7}
...
range: 119.5 ± 48.5
average: 1026/10
...
{153,3}
{168,2}

string coincidence

71: {5,7}

2-digit strings

{1300,91}
{1416,07}
...
range: 2399.5 ± 1099.5
average: 215386/100
...
{3493,28}
{3499,95}

string coincidence

2146: {33,48}

3-digit strings

{20589,141}
{20729,713}
...
range: 37290.5 ± 16701.5
average: 28860154/1000
...
{51375,552}
{53992,661}

string coincidences

22044: {024,275}
24486: {404,675}
25305: {410,947}
25440: {317,604}
25668: {442,815}
25704: {123,766}
25980: {096,868}
26046: {378,588}
26136: {422,677}
26316: {227,929}
26477: {152,690}
26695: {085,256}
26792: {048,732}
27003: {737,974}
27121: {545,932}
27479: {183,687}
28196: {300,554}
28252: {116,641}
28270: {099,575}
28317: {578,656}
28425: {287,392}
28532: {171,910}
28609: {017,919}
28784: {033,719}
28850: {164,647}
28891: {346,505}
29173: {648,787}
29705: {668,997}
29711: {335,799}
29976: {665,995}
30977: {131,395}
32637: {076,426}
33550: {555,796}
33607: {582,598}
33631: {117,735}
39571: {021,622}

4-digit strings

{266774,6355}

{273317,4949}

...

range: 459917 ± 193143

average: 3642758125/10000

...

{625874,6636}

{653060,6164}

string coincidences

296341: {0317,9730}

299582: {2041,2103}

302068: {8362,9844}

303160: {1883,2335}

304631: {5262,7194}

304639: {2896,5816}

305663: {5142,5397}

307552: {0904,8968}

307739: {9064,9656}

308220: {2396,6102}

308408: {5509,8025}

308917: {0658,5181}

309422: {2879,8852}

310452: {2800,6576}

310789: {0093,5900}

311943: {4436,7337}

312480: {5954,9044}

312956: {1741,1944}

313628: {7855,9582}

314127: {4003,6689}

315423: {6059,6252}

315844: {3119,7155}

316864: {2825,4655}

317042: {0507,0655}

318106: {7886,9390}

318428: {1872,4548}

318594: {5091,5501}

318703: {0505,6814}

319722: {7009,7541}

320081: {0089,1201}

320549: {4780,9688}

321025: {0020,8594}

321026: {1045,1488}

321108: {2364,3963}

322286: {5390,9872}

322907: {5976,9894}

323025: {3082,5477}

323178: {4438,7411,9268}

323872: {5264,8601}

323973: {7651,9051}

324814: {4462,4521}

324885: {4116,8104}

326420: {5641,8345}

326585: {0703,3413}

326793: {7640,9369}

326886: {3632,7622}

327005: {7087,8412}

327241: {0013,4113}

327387: {2757,6279}

327406: {8469,9238}

327692: {0328,1158}

327856: {6037,7447}

327899: {2569,8404}

328022: {2068,8665}

328433: {3715,9685}

328441: {4541,5491}

328592: {1770,7600}

329117: {2725,3266,7959}

329142: {1846,7235}

329285: {0324,7893}

329773: {1510,6807}

329834: {3380,5873}

330434: {5197,8702}

330442: {0232,8274}

330690: {4111,6761}

331061: {3225,5929}

331358: {2540,7253}

331463: {1493,9185}

331571: {1174,7276}

331610: {8690,9273}

332045: {1192,9701}

332136: {2114,8049}

332481: {1728,5967}

332507: {4609,5093}

332627: {0126,2700}

333146: {2636,5860}

333450: {8609,9537}

333462: {5600,8478}

333663: {1050,7693}

333682: {8270,9353}

333998: {4034,7687}

334303: {3254,4714}

334617: {6586,7828}

334837: {2030,8091}

334914: {9034,9881}

335184: {3039,6080}

335216: {5066,9474}

335580: {4004,4864}

335618: {5891,9991}

335647: {4715,9359}

335648: {1060,3150}

335833: {0604,9269}

335867: {5145,8779}

336146: {7404,8354}

336846: {2783,4059}

337394: {0750,7595}

337524: {5159,9199}

338108: {4509,6866}

338157: {2741,4933}

338377: {1494,2094}

338420: {1515,3966}

338794: {9594,9845}

339154: {0743,9414}

339356: {1476,5817}

340009: {2933,8133}

340042: {2953,9957}

340097: {0172,1204}

340281: {5404,8419}

340472: {0060,3472}

340926: {0872,6788}

341131: {0237,6434,8154}

341157: {1810,9578}

341370: {5676,5786}

341506: {1432,6014}

341528: {3645,7689}

341902: {2203,6407}

341914: {5194,8521}

341983: {6118,7811}

342019: {2264,5218}

342233: {3949,5461}

342260: {0897,8605}

342394: {0260,8494}

342564: {4002,9173}

342630: {5527,8773}

342757: {3569,9032}

342821: {4799,5993}

343798: {7343,8491}

344003: {5961,7381}

344041: {2518,3260}

344251: {0102,3745}

344396: {1523,4810}

344780: {9627,9882}

345245: {1558,7972}

345278: {8163,9325}

345602: {4701,5555}

345933: {4788,9070}

345936: {1277,4166}

346134: {2839,8391}

346151: {0856,3654}

346219: {5495,5683}

346364: {4192,7639}

346769: {0587,1635,2374}

347036: {0559,8406}

347161: {8907,9741}

347522: {3605,3996}

347620: {2511,6244}

347740: {0579,8606}

347746: {4358,8878}

347775: {8741,9906}

347907: {2204,9640}

347925: {5423,6137}

348332: {6774,8667}

348762: {3488,6962}

348855: {0956,2340}

348911: {3646,9581}

349048: {3546,3744}

349073: {4179,8338}

349254: {3805,6726}

349471: {1047,4986}

349829: {6157,7860}

350183: {2142,6961,9708}

350308: {4130,6670}

350516: {4296,8527}

350569: {4060,9635}

350635: {1378,2927}

350684: {1261,7773}

351243: {1769,3536}

351326: {3121,7915}

351529: {2380,6571}

351561: {3911,5291}

351713: {2415,8585}

352134: {0692,1374}

352235: {5647,6629}

352294: {7046,8069}

352417: {0619,5419}

352438: {2439,8199}

352539: {6748,8705}

352694: {1180,7163}

353011: {2131,6621}

353082: {0174,4600}

353168: {1889,5682}

353239: {4050,9956}

353464: {2294,4966}

353828: {4931,7372}

353840: {0217,0907}

354455: {3776,6185}

355087: {4417,6577}

355188: {3510,5193}

355324: {0017,2318}

355402: {6057,7503}

355434: {3307,6790}

355805: {2138,3581}

355947: {1746,6743}

356094: {2159,6092}

356103: {2035,2615}

356255: {7001,8420}

356497: {1586,2339}

356516: {0066,0762}

356620: {3657,4174}

356900: {2055,5223}

356973: {8776,9103}

357223: {1687,7664}

358009: {7382,7497}

358487: {1366,4133}

359062: {1146,8147}

359220: {3660,8822}

359230: {6165,8191}

359616: {0633,6176}

360109: {2307,7362}

360826: {3455,7078}

361585: {4828,9217}

361678: {3837,7685}

362060: {0732,5850}

362094: {4434,8748}

362106: {2659,8340}

362129: {1302,2693,3550,9945}

362530: {2483,3015}

362580: {1281,5708}

362896: {4255,7722}

362924: {4744,9644}

363104: {0674,3672}

363222: {3484,7142}

363547: {2239,5260}

363885: {6291,7596}

363897: {2848,4773}

364027: {1035,8633}

364036: {7200,8926}

364503: {0589,5054}

364986: {0798,8765}

365010: {0005,8973}

365249: {5474,7459}

365443: {0073,7884}

365632: {1824,7237}

365776: {0071,8921}

365966: {0244,7492}

365968: {4984,5128}

365996: {7230,9404}

366225: {1300,3345}

366355: {9461,9915}

367072: {1481,5969}

367111: {2634,6306}

367217: {2393,2429}

367898: {4498,8180}

368443: {5085,7256}

368694: {5507,8283,9984}

368976: {6996,7062,7667}

369313: {2716,8640}

369495: {4545,7392}

369970: {2764,5011}

370814: {4601,6747}

370974: {4575,5613}

371553: {2804,6497}

372064: {6702,8361}

372108: {2949,7989}

372252: {1248,7907}

372311: {0050,5804}

372356: {4343,8399}

372357: {1716,7165}

372814: {6287,7363}

373523: {4530,8105}

373861: {3379,4697}

374797: {5925,8296}

374810: {1433,9562}

375824: {2284,6196}

376003: {1052,8083}

376138: {4294,7424}

376739: {9078,9973}

376760: {2051,9750}

376785: {0438,7605}

377455: {4277,5315}

378037: {2196,7421}

378355: {2938,9245}

378973: {2147,9852}

378984: {0276,6941}

379462: {0014,8562}

379612: {0680,5393}

379782: {1791,2266}

380544: {1328,8863}

381077: {7870,9296}

381177: {2894,7066}

381669: {0006,5820}

381849: {0597,5625}

382182: {3690,4675}

382940: {3346,8450}

383096: {4242,6254}

383242: {2584,7346}

383783: {3804,9176}

383870: {3557,9628}

384280: {1068,7269}

384385: {2436,4817}

384511: {3194,6645}

384649: {0881,6310}

385168: {4726,5116}

385543: {2545,8762}

386204: {9665,9773}

386294: {0727,1169}

387984: {5505,9448}

388202: {5985,8507}

389330: {1857,9447}

389349: {2841,5269}

389481: {2729,3998}

389795: {2367,4654}

389853: {1809,9849}

390037: {5162,5844}

390708: {0628,9706}

391278: {5899,7553}

391837: {2013,8526}

391929: {1713,3793}

392002: {2034,2872}

392518: {7118,9658}

393878: {5496,9517}

396142: {6936,8249}

396567: {7081,8211}

396886: {3938,8909}

397399: {0352,2680}

397503: {5059,9082}

397631: {1691,7111}

398347: {1367,5590}

398451: {2077,3116}

398583: {0687,9055}

398635: {4387,6361}

401346: {0266,4432}

402139: {5528,6893}

402315: {0936,7464}

403677: {3809,8263}

405493: {6027,6698}

407926: {0891,6640}

412908: {0278,3055}

413260: {0749,9602}

413732: {6654,7788}

414179: {8067,8580}

415732: {0870,6078}

416017: {0320,5720}

417139: {1126,9616}

417664: {4785,6195}

419623: {3402,3883}

420795: {1676,6722}

421861: {0786,1291}

423699: {3309,8888}

426750: {7638,9766}

433287: {1151,7375}

441637: {2651,2822}

452674: {3564,8663}

504659: {3418,3774}

514562: {0052,1787}

The red numbers in the summaries for each n-digit result has become a sequence: A360623.