A103357 Numbers n such that n and pi(n) (A000720) are palindromic.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 262, 323, 393, 525, 535, 555, 666, 818, 878, 949, 2002, 3773, 5775, 6116, 13031, 19591, 39093, 41414, 47374, 59295, 63236, 81918, 94549, 95759, 252252, 394493, 594495, 662266, 674476, 686686, 698896, 764467

Offset: 1

Author

Zak Seidov, Feb 02 2005

Keywords

• base
• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..196 (terms < 10^16)

Crossrefs

Corresponding palindromic pi(n) in A103358.

Cf. A046941, A046942, A103358, 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}]; a (* Robert G. Wilson v, Feb 03 2005 *)

Formula

a(n) = P_A103358(n).

Extensions

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