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A247122 Primes p such that the digit sum of p is an odd composite number.

%I A247122 #17 Feb 21 2016 10:55:24
%S A247122 997,1699,1789,1879,1987,2689,2797,2887,3499,3697,3769,3877,3967,4597,
%T A247122 4759,4957,4993,5479,5569,5659,5749,5839,5857,6199,6379,6397,6469,
%U A247122 6577,6793,6829,6883,6991,7297,7369,7459,7477,7549,7639,7873,7927,7963,8089,8179,8269,8287,8377,8467,8539,8629,8647,8719,8737,8863,8971,8999
%N A247122 Primes p such that the digit sum of p is an odd composite number.
%C A247122 Motivation from James Grime: "What is the smallest prime with digital sum odd, but not prime?"
%C A247122 This sequences differs from A106763 at a(55) = 8999.
%C A247122 The digit sums are multiples of primes > 3. If the digit sum is a multiple of 3, the number itself cannot be prime.
%C A247122 The first odd composite digit sums are 25 (first occurrence is for 997), 35 (first occurrence is for 8999), 49 (first occurrence is for 598999), 55 (first occurrence is for 2998999), 65 (first occurrence is for 29999999), 77 (first occurrence is for 699899999) ...
%H A247122 Michael De Vlieger, <a href="/A247122/b247122.txt">Table of n, a(n) for n = 1..10000</a>
%e A247122 997 is prime but its digit sum is 25, which is odd and composite. So 997 is a member of this sequence.
%t A247122 a247122[n_Integer] := Flatten@Last@Reap[Module[{i, digitSum}, digitSum[x_] := Plus @@ IntegerDigits[x]; For[i = 1, i < n,
%t A247122 If[OddQ[digitSum[Prime[i]]] && CompositeQ[digitSum[Prime[i]]],
%t A247122 Sow[Prime[i]], Null], i++]]]; a247122[1200] (* _Michael De Vlieger_, Nov 29 2014 *)
%t A247122 dsocQ[n_]:=Module[{s=Total[IntegerDigits[n]]},OddQ[s]&&CompositeQ[s]]; Select[Prime[Range[1200]],dsocQ] (* _Harvey P. Dale_, Feb 21 2016 *)
%o A247122 (PARI) forprime(p=1,10^4,if(!isprime(sumdigits(p))&&sumdigits(p)%2,print1(p,", ")))
%Y A247122 Cf. A106763, A007953.
%K A247122 nonn,base,easy
%O A247122 1,1
%A A247122 _Derek Orr_, Nov 19 2014