A046941 Palindromic primes whose indices n are also palindromes.

2, 3, 5, 7, 11, 143787341, 11853735811, 126537757735621

Offset: 1

Author

Carlos Rivera

Keywords

• nonn
• base
• more

Links

• Chris K. Caldwell and G. L. Honaker, Jr., 143787341
• Carl Pomerance, What we still don't know about addition and multiplication, Trjitzinsky Lecture 1, U. Illinois Urbana-Champaign, November 27, 2018. See slides 22 & 24.
• Eric Weisstein's World of Mathematics, Palindromic Prime.

Crossrefs

Cf. A046942, A103357, 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; Do[p = NextPalindrome[p]; While[ !PrimeQ[p], p = NextPalindrome[ p]]; q = IntegerDigits[ PrimePi[ p]]; If[Reverse[q] == q, Print[{p, FromDigits[q]}]], {n, 10^4}] (* Robert G. Wilson v, Feb 03 2005 *)
palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t = {}; Do[p = Prime[i]; If[palQ[i] && palQ[p], AppendTo[t, p]], {i, 9*10^6}]; t (* Jayanta Basu, Jun 23 2013 *)

PARI

ispal(n) = my(d=digits(n)); d == Vecrev(d);
isok(p) = isprime(p) && ispal(p) && ispal(primepi(p)); \\ Michel Marcus, Jan 27 2019

Formula

a(n) = prime(A046942(n)).

Extensions

a(7) from Giovanni Resta, May 14 2003

a(8) from Giovanni Resta, Aug 10 2019