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

Author

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

Keywords

• base
• nonn

Examples

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

Crossrefs

Cf. A083816.

Programs

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}]