A103403 Palindromic primes q derived from palindromes p such that pi(p) = q.

2, 2, 3, 3, 5, 11, 101, 151, 757, 797, 72727, 3485843, 7362637, 753535357, 32792329723, 1644209024461, 9600458540069, 125319848913521, 164957666759461

Offset

1,1

Comments

From a suggestion from Zak Seidov, Feb 02 2005.

a(16) > pi(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, q]]], {n, 10^6}]; a
palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t = {}; Do[If[palQ[n] && PrimeQ[y = PrimePi[n]] && palQ[y], AppendTo[t, y]], {n, 10^6}]; t (* Jayanta Basu, Jun 24 2013 *)

Crossrefs

Cf. A046941, A046942, A103357, A103358, A103402.

Sequence in context: A243927 A102330 A103598 * A052473 A165122 A240505

Adjacent sequences: A103400 A103401 A103402 * A103404 A103405 A103406

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