A099744 -id:A099744 - cp's OEIS frontend

A099746 Primes arising in A099744.

10301, 10501, 10601, 1022201, 1028201, 1035301, 1043401, 1055501, 1062601, 1065601, 1074701, 1082801, 1085801, 1092901, 1093901, 101030101, 101060101, 101141101, 101171101, 101282101, 101292101, 101343101, 101373101, 101414101

Offset: 1

N. J. A. Sloane, Nov 19 2004

Prompted by Harvey Dubner's Nov 07 2004 discovery that 10000...000M000...00001 with M=3761673, a palindrome, is a 130023-digit palindromic prime.

Cf. A099744, A100026, A100027.

p = Select[ Range[ 22322], # == FromDigits[ Reverse[ IntegerDigits[ # ]]] &]; q = Select[p, PrimeQ[ FromDigits[ Join[{1, 0}, IntegerDigits[ # ], {0, 1}]]] &]; Table[ FromDigits[ Join[{1, 0}, IntegerDigits[ q[[n]]], {0, 1}]], {n, 24}]; (* Robert G. Wilson v, Nov 20 2004 *)

More terms from Robert G. Wilson v, Nov 20 2004

A100026 Consider all (2n+1)-digit palindromic primes of the form 10...0M0...01 (so that M is a palindrome with <= 2n-1 digits); a(n) = smallest such M.

Original entry on oeis.org

0, 3, 3, 3, 5, 8, 323, 5, 8, 212, 3, 161, 8, 3, 242, 3, 8, 10901, 737, 161, 242, 333, 282, 6, 252, 474, 5, 12921, 8, 131, 18381, 6, 444, 6, 797, 606, 717, 15351, 464, 333, 626, 545, 13031, 161, 747, 191, 323, 636, 32523, 303, 282, 888, 686, 18981, 111, 15951, 12021

Offset: 1

Harvey Dubner (harvey(AT)dubner.com), Nov 20 2004

Is this the same as "Longest palindromic proper substring of A100027(n) or A028989(n+1) that occurs only once in the decimal representation of A100027(n) or A028989(n+1), respectively"? - Felix Fröhlich, Apr 30 2022

A more formal definition may be a(n) = A004151(A028989(n+1) - 10^(2n) - 1) with the convention that A004151(0) = 0. Only in the unlikely situation that A080176 contains undiscovered primes will a(n) = 0 occur for n > 1. - Jeppe Stig Nielsen, Apr 04 2025

Chai Wah Wu, Table of n, a(n) for n = 1..1000

The corresponding palindromic primes are shown in A100027.

Cf. A028989, A099744, A099746, A100028.

f[n_] := Block[{k = 0, t = Flatten[Join[{1}, Table[0, {n - 1}]]]}, While[s = Drop[t, Min[ -Floor[ Log[10, k]/2], 0]]; k != FromDigits[ Reverse[ IntegerDigits[k]]] || !PrimeQ[ FromDigits[ Join[s, IntegerDigits[k], Reverse[s]]]], k++ ]; k]; Table[ f[n], {n, 56}] (* Robert G. Wilson v, Nov 22 2004 *)

More terms from Robert G. Wilson v, Nov 22 2004

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A099746 Primes arising in A099744.

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