A103402 Palindromes p such that pi(p) is a palindromic prime.

3, 4, 5, 6, 11, 33, 555, 878, 5775, 6116, 919919, 58633685, 129707921, 16958285961, 867275572768, 50166722766105, 310439747934013, 4384495885944834, 5817988338897185

Offset

1,1

Comments

From a suggestion from Zak Seidov, Feb 02 2005.

a(16) > 32*10^12. - Donovan Johnson, Dec 03 2009

Links

Table of n, a(n) for n=1..19.

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 = PrimePi[p]; If[PrimeQ[q], r = IntegerDigits[q]; If[Reverse[r] == r, Print[{p, q}]; AppendTo[a, p]]], {n, 10^6}]; a
palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t = {}; Do[If[palQ[n] && PrimeQ[x = PrimePi[n]] && palQ[x], AppendTo[t, n]], {n, 10^6}]; t (* Jayanta Basu, Jun 24 2013 *)

Crossrefs

Cf. A046941, A046942, A103357, A103358, A103403.

Sequence in context: A048989 A356050 A299299 * A154664 A371242 A366743

Adjacent sequences: A103399 A103400 A103401 * A103403 A103404 A103405

Keyword

nonn,base,more

Author

Robert G. Wilson v, Feb 03 2005

Extensions

a(15) from Donovan Johnson, Dec 03 2009

a(16)-a(17) from Chai Wah Wu, Sep 04 2019

a(18)-a(19) from Giovanni Resta, Sep 12 2019

Status

approved