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Iterated sum-of-digits of palindromic prime; or digital root of palindromic prime.
7

%I #9 Sep 09 2015 05:14:30

%S 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,

%T 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,

%U 2,8,7,1,2,1,7,2,7,2,4,8,4,2,2,2,5,4

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

%C 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.

%H Shyam Sunder Gupta, <a href="/A229875/b229875.txt">Table of n, a(n) for n = 1..5953</a>

%F a(n) = A010888(A002385(n)). - _R. J. Mathar_, Sep 09 2015

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

%t 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]

%Y Cf. A038194, A002385.

%K nonn,base,less

%O 1,1

%A _Shyam Sunder Gupta_, Oct 02 2013