A103405 The 2^n-th palindromic prime.

2, 3, 7, 151, 757, 14341, 36563, 1114111, 1793971, 7256527, 115737511, 188646881, 746676647, 11984748911, 19541414591, 75174747157, 1192238322911, 1901840481091, 7382419142837, 115344262443511, 181836161638181

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Example

2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727 and 757 are the first sixteen palindromic primes.

Mathematica

NextPalindrome[n_] := Block[ {lg = Floor@ Log[10, n] + 1, idn = IntegerDigits@ n}, If[ Union@ idn == {9}, Return[n + 2], If[lg < 2, Return[n + 1], If[ FromDigits@ Reverse@ Take[ idn, Ceiling[lg/2]] > FromDigits@ Take[ idn, -Ceiling[lg/2]], FromDigits@ Join[ Take[ idn, Ceiling[lg/2]], Reverse@ Take[ idn, Floor[lg/2]]], idfhn = FromDigits@ Take[ idn, Ceiling[lg/2]] + 1; idp = FromDigits@ Join[ IntegerDigits@ idfhn, Drop[ Reverse@ IntegerDigits@ idfhn, Mod[lg, 2]]] ]]]];
c = 0; pal = 0; Do[ While[c < 2^n, pal = NextPalindrome@ pal; If[ PrimeQ@ pal, c++ ]]; Print@ pal, {n, 0, 20}]

Crossrefs

Cf. A083816.

Sequence in context: A088856 A173913 A007013 * A087311 A053924 A130060

Adjacent sequences: A103402 A103403 A103404 * A103406 A103407 A103408

Keyword

base,nonn

Author

Robert G. Wilson v, Feb 04 2005, corrected Nov 16 2006

Status

approved