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%I #9 Sep 08 2022 08:45:50
%S 1,1,1,1,1,3,2,5,1,1,7,2,1,1,1,2,5,1,1,6,2,2,1,1,4,1,4,2,2,1,2,1,1,1,
%T 2,1,1,4,6,1,1,2,1,1,1,1,3,1,1,1,5,6,1,4,4,1,1,2,2,1,1,4,3,1,1,1,1,1,
%U 8,2,1,1,2,1,1,5,2,1,1,1,8,1,4,2,3,1,1,2,1,1,1,4,1,8,3,2,6,2,3,6,2,1,10,8,1
%N Smallest k such that sum of digits of prime(n)^k is prime.
%C For all n, prime(n)^0 = 1 has nonprime sum of digits 1.
%C a(n) = 1 iff prime(n) is in A046704, an additive prime. a(n) = 1 iff n is in A075177.
%e prime(1) = 2; 2^1 = 2 has prime sum of digits 2. Hence a(1) = 1.
%e prime(6) = 13; 13^1 = 13 has nonprime sum of digits 4; 13^2 = 169 has nonprime sum of digits 16; 13^3 = 2197 has prime sum of digits 19. Hence a(6) = 3.
%t sdp[n_]:=Module[{k=1},While[!PrimeQ[Total[IntegerDigits[Prime[n]^k]]], k++]; k]; Array[sdp,110] (* _Harvey P. Dale_, Apr 13 2014 *)
%o (Magma) S:=[]; for n in [1..105] do j:=1; while not IsPrime(&+Intseq(NthPrime(n)^j)) do j+:=1; end while; Append(~S, j); end for; S;
%Y Cf. A046704, A075177, A172035.
%K base,nonn
%O 1,6
%A _Klaus Brockhaus_, Jan 29 2010
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