wordthreepeating

1, 21, 1000013, 4000414, 131256, 21445566, ________________.

Coverage

BBC news anchor this morning: "Give us the background to it. What's at the centre of it?"

Flagpole

oneseventhreesixfiveeleveneightninetwothirteenfourtentwelvesixteenfifteentwentysixfourteeneighteenseventeennineteentwentyonehundredeleventwentyonetwentyfivetwentytwotwentythreetwentyfourtwentyeightthirtyeightthirtytwentyseventwentyninethirtyonethirtyseventhirtythreethirtytwofortytwothirtyfourthirtyfivethirtysixthirtyninefortyfortyonefortythreefortyfivefortysevenfortyfourfortysixfiftyfourfortyeightfortyninefiftyonefiftysevenfiftyfiftytwofiftythreeonehundredtwelvefiftyfivefiftyeightfiftysixfiftyninesixtysixtyonesixtythreesixtyfivesixtysevensixtyfoursixtytwoseventyfoursixtysixsixtyeightsixtynineseventyseventyoneseventytwoseventythreeseventyfiveseventysixseventysevenseventyeightseventynineeightysixeightyfoureightyoneninetyfoureightythreeeightyeightytwoeightyfiveeightyseveneightyeighteightynineninetyeightninetythreeninetyninetyoneninetytwoninetyfiveninetysixninetysevenonehundredfiveninetynineonehundredonehundredtwoonehundredoneonehundredthreeonehundredfouronehundredsixonehundredeightonehundredsevenonehundrednineonehundredtenonehundredthirteen...

This is the top of the flagpole of Eric Angelini's English flagpole sequence. If we subtract the indices from the sequence, we get: 0, 5, 0, 2, 0, 5, 1, 1, -7, 3, -7, -2, -1, 2, 0, 10, -3, 0, -2, -1, -1, 89, -2, 1, -3, -3, -3, 0, 9, 0, -4, -3, -2, 3, -2, -4, 5, -4, -4, -4, -2, -2, -2, -1, 0, 1, -3, -2, 5, -2, -2, -1, 4, -4, -3, -3, 55, -3, -1, -4, -2, -2, -2, -1, 0, 1, -3, -6, 5, -4, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, 4, 1, -3, 9, -3, -7, -6, -4, -3, -3, -3, 5, -1, -5, -5, -5, -3, -3, -3, 4, -3, -3, -2, -4, -3, -3, -2, -1, -3, -2, -2, 0, ... Herein, the positions of the zeros are: 1, 3, 5, 15, 18, 28, 30, 45, 65, 113, ... In effect, these are the indices of the flagpole sequence where a(n) = n. It turns out that the majority of flagpole sequence numbers lie on that line — of the first 1000000 terms, 688153. Within this region, the largest spacing between consecutive on-the-line terms is between term #321947 (=321947) and term #411273 (=411273). This large gap is due to the demand for the letter L exceeding the local supply. A much larger gap will begin ~10^9 when demand for the letter M exceeds its local supply.

Bye bye Birdo

Just a few hours shy of a 492-day stay with us, Harry Vance attempts to put a reluctant Birdo into her carrier. I will miss her anticipation of the microwave beep, half-way (or so) through my one-minute milk heat-ups, and the imitation squeaks as the window blind by her cage came up in the morning. Birdo's vocal repertoire included coughing, sneezing, and a hearty nose-blowing whenever I brought a hankie up to my face. She arrived with a couple of well-worn, two-note whistles but Catherine eventually taught her the theme to The Andy Griffith Show, which fell into disuse after I taught her I Was Kaiser Bill's Batman — phrases of which became our back-and-forth contact calling. She could do a sparrow, robin, or gull, a cat or a dog, and would not hesitate to join in at the first hint of laughter. Birdo's "English" included yeap (guessing correctly, occasionally, the answer to a query being asked of someone else), naow (said with a snarl), c'mere, c'mon, good girl, and of course Har-ree followed by — in a different voice — Birdo. She had a mock people-speak but the monologue was largely unintelligible. Catherine tried once to get her to do a happy wheee but it came out incredibly cranky when she finally succumbed to it. Birdo would greet you with a cluck and thank you with a coo. When she really wanted your attention, she'd let out an ear-piercing smoke-alarm. She had an impossible-to-describe, funny bit that we called the 'dying-parrot'. Watching her grapple with falling-asleep had me conjecture that birds evolved the behaviour to rest on one leg, with the head tucked into the back, so as to make the mathematics/mechanics of balancing that much easier. (I'm aware of the heat-loss theory but I'm not buying it as anything more than a modest advantage in limited circumstances. On the other hand, trying to maintain one's balance with a minimum of thought/correction is, high up — where a bird is likely to find itself at night, a matter of some gravity.) As for having a parrot as a room-mate, I'm now aware of how much dander and feather fluff (such) a bird generates each and every day and this detritus becomes a cleaning-burden far beyond the confines of the cage.