A124232 Numbers n such that prime(n) and pi(n) are palindromic.

1, 2, 3, 4, 5, 26, 32, 36, 138, 3691, 6987, 7193, 86969, 117766, 127150, 142583, 515786, 531448, 539596, 615980, 646060, 17262354, 39816443, 47548105, 48803361, 49426747, 528977302, 538348374, 1475057753, 1559827952, 2994135736, 60040412496, 64516992534, 333771325433, 11655934712628, 21872729899659, 22903935103276, 28311805106395, 29606335619415

Offset: 1

Author

Tanya Khovanova, Dec 13 2006

Keywords

• base
• nonn

Crossrefs

Subsequence of A075807 = numbers n such that n-th prime is palindromic.

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]]] ]]]];
palQ[n_Integer] := Module[{idn = IntegerDigits@n}, idn == Reverse@ idn]; lst = {}; k = 1; While[k < 10^12, If[ PrimeQ@k && palQ@PrimePi@PrimePi@k, Print@PrimePi@k; AppendTo[lst, PrimePi@k]]; k = NextPalindrome@k]; lst (* Robert G. Wilson v *)

Extensions

a(22) - a(31) from Robert G. Wilson v, Dec 14 2006

a(32)-a(33) from Donovan Johnson, Jul 19 2012

a(34) from Chai Wah Wu, Sep 12 2019

a(35)-a(39) from Chai Wah Wu, Sep 19 2019