A229875 Iterated sum-of-digits of palindromic prime; or digital root of palindromic prime.

2, 3, 5, 7, 2, 2, 5, 7, 1, 2, 7, 2, 4, 5, 7, 1, 4, 5, 1, 2, 5, 7, 8, 7, 8, 1, 4, 5, 2, 7, 8, 4, 8, 7, 8, 5, 8, 1, 2, 2, 7, 1, 4, 5, 1, 2, 7, 8, 1, 4, 5, 8, 4, 4, 5, 8, 1, 4, 7, 8, 1, 5, 2, 5, 4, 7, 4, 5, 2, 8, 7, 1, 2, 1, 7, 2, 7, 2, 4, 8, 4, 2, 2, 2, 5, 4

Offset

1,1

Comments

Integers with digital root 3, 6 or 9 are divisible by 3, so 3 is the only palindromic prime with digital root 3 and there are no palindromic primes with digital root 6 or 9.

Links

Shyam Sunder Gupta, Table of n, a(n) for n = 1..5953

Formula

a(n) = A010888(A002385(n)). - R. J. Mathar, Sep 09 2015

Example

a(7)=5 because the 7th palindromic prime is 131 and 1+3+1 = 5.

Mathematica

t = {}; Do[z = n*10^(IntegerLength[n] - 1) + FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[z], AppendTo[t, Mod[z, 9]]], {n, 1, 99999}]; Insert[t, 2, 5]

Crossrefs

Cf. A038194, A002385.

Sequence in context: A142711 A357096 A093338 * A230199 A275542 A187559

Adjacent sequences: A229872 A229873 A229874 * A229876 A229877 A229878

Keyword

nonn,base,less

Author

Shyam Sunder Gupta, Oct 02 2013

Status

approved