Wednesday, March 30

Near-rep-nine palindromic primes

On Sunday, I gave two large (Darren Bedwell) examples of numbers in A088284. That sequence has been languishing for over ten years with only eight terms! So here (culled from Makoto Kamada's webpages) are forty more:

 1 10^3-8*10^1-1
 2 10^3-7*10^1-1
 3 10^11-8*10^5-1
 4 10^17-7*10^8-1
 5 10^19-7*10^9-1
 6 10^27-8*10^13-1
 7 10^29-5*10^14-1
 8 10^45-5*10^22-1
 9 10^53-10^26-1
10 10^73-5*10^36-1
11 10^87-8*10^43-1
12 10^177-4*10^88-1
13 10^209-5*10^104-1
14 10^225-4*10^112-1
15 10^237-2*10^118-1
16 10^339-8*10^169-1
17 10^363-8*10^181-1
18 10^397-4*10^198-1
19 10^705-7*10^352-1
20 10^757-10^378-1
21 10^1061-7*10^530-1
22 10^1245-4*10^622-1
23 10^1395-7*10^697-1
24 10^2273-5*10^1136-1
25 10^2493-10^1246-1
26 10^2631-7*10^1315-1
27 10^3159-8*10^1579-1
28 10^3597-10^1798-1
29 10^3837-7*10^1918-1
30 10^5749-7*10^2874-1
31 10^5835-10^2917-1
32 10^8457-4*10^4228-1
33 10^11753-7*10^5876-1
34 10^13537-7*10^6768-1
35 10^20105-4*10^10052-1
36 10^35729-5*10^17864-1
37 10^36155-8*10^18077-1
38 10^45305-8*10^22652-1
39 10^46069-10^23034-1
40 10^50897-5*10^25448-1
41 10^95019-10^47509-1
42 10^104281-10^52140-1
43 10^111725-4*10^55862-1
44 10^125877-7*10^62938-1
45 10^134809-10^67404-1
46 10^269479-7*10^134739-1
47 10^290253-2*10^145126-1
48 10^314727-8*10^157363-1

I cannot guarantee that the last three (Darren Bedwell terms) are contiguous with the first 45 because Kamada's stated search range for that second power of ten is only up to 68000.

I've also now watched the Numberphile Glitch Primes and Cyclops Numbers video. Glitch primes are the not-quite-palindromic near-rep-nine numbers with which I started Sunday's post. Just prior to defining the (strictly base-two) Cyclops numbers (@ 9:33) we are told that 10^19-10^9-1 is a prime! Looking at my above table, 10^53-10^26-1 should have been the example used.

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