A103358 Palindromes q derived from palindromes p such that pi(p) = q.

0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 8, 11, 55, 66, 77, 99, 99, 101, 121, 141, 151, 161, 303, 525, 757, 797, 1551, 2222, 4114, 4334, 4884, 5995, 6336, 8008, 9119, 9229, 22222, 33433, 48684, 53735, 54645, 55555, 56465, 61316, 64046, 72027, 72727, 84548, 89998

Offset: 1

Author

Zak Seidov, Feb 02 2005

Keywords

• base
• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..196

Crossrefs

Equals pi(A103357).

Cf. A046941, A046942, A103357, A103402, A103403.

Programs

Mathematica

NextPalindrome[n_] := Block[ {l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[ idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[ idn, Ceiling[l/2]]]] FromDigits[ Take[ idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[ idn, Ceiling[l/2]], Reverse[ Take[ idn, Floor[l/2]]] ]], idfhn = FromDigits[ Take[ idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[ idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]]]] ]]]];
p = 0; a = {}; Do[p = NextPalindrome[ p]; q = IntegerDigits[ PrimePi[ p]]; If[ Reverse[q] == q, Print[{p, FromDigits[q]}]; AppendTo[a, p]], {n, 10^4}]; PrimePi[a] (* Robert G. Wilson v, Feb 03 2005 *)

Extensions

More terms from Robert G. Wilson v, Feb 03 2005