A172216 Smallest k such that sum of digits of prime(n)^k is prime.

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, 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, 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

Offset: 1

Author

Klaus Brockhaus, Jan 29 2010

Keywords

• base
• nonn

Comments

For all n, prime(n)^0 = 1 has nonprime sum of digits 1.

a(n) = 1 iff prime(n) is in A046704, an additive prime. a(n) = 1 iff n is in A075177.

Examples

			prime(1) = 2; 2^1 = 2 has prime sum of digits 2. Hence a(1) = 1.
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.
		

Crossrefs

Cf. A046704, A075177, A172035.

Programs

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;

Mathematica

sdp[n_]:=Module[{k=1},While[!PrimeQ[Total[IntegerDigits[Prime[n]^k]]], k++]; k]; Array[sdp,110] (* Harvey P. Dale, Apr 13 2014 *)