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

Author

Shyam Sunder Gupta, Oct 02 2013

Keywords

• nonn
• base
• less

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.

Examples

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

Links

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

Crossrefs

Cf. A002385, A010888, A038194.

Programs

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]
Mod[#,9]&/@Select[Prime[Range[9000]],PalindromeQ] (* Harvey P. Dale, Mar 25 2025 *)

Formula

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