A099746 -id:A099746 - cp's OEIS frontend

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.

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

A099744 Palindromes n such that 10n01 is a prime.

Original entry on oeis.org

3, 5, 6, 222, 282, 353, 434, 555, 626, 656, 747, 828, 858, 929, 939, 10301, 10601, 11411, 11711, 12821, 12921, 13431, 13731, 14141, 14241, 14741, 15951, 16161, 17171, 17771, 18381, 18981, 19191, 19491, 19991, 20402, 20702, 22022, 22322

Offset: 1

N. J. A. Sloane, Nov 19 2004

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A002113, A099746, A032672, A099720, A100026, A100027.

read transforms; pal:=[]; for n from 0 to 8000 do if digrev(n) = n then pal:=[op(pal),n]; fi; od:
t0:=[]; u0:=[]; for n from 1 to nops(pal) do m:=pal[n]; p0:="10"; p1:="01"; t1:=cat(p0,m,p1); t1:=convert(t1,decimal,10); if isprime(t1) then t0:=[op(t0),m]; u0:=[op(u0),t1]; fi; od: t0; # u0 gives A099746.

p = Select[ Range[ 22322], # == FromDigits[ Reverse[ IntegerDigits[ # ]]] &]; Select[p, PrimeQ[ FromDigits[ Join[{1, 0}, IntegerDigits[ # ], {0, 1}]]] &] (* Robert G. Wilson v, Nov 20 2004 *)
Select[Range[23000],PalindromeQ[#]&&PrimeQ[FromDigits[Join[{1,0},IntegerDigits[ #],{0,1}]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 26 2021 *)

More terms from Robert G. Wilson v, Nov 19 2004

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions