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

1,6

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.

Links

Table of n, a(n) for n=1..105.

Example

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.

Mathematica

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

Prog

(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;

Crossrefs

Cf. A046704, A075177, A172035.

Sequence in context: A368744 A291455 A248849 * A121490 A197293 A099643

Adjacent sequences: A172213 A172214 A172215 * A172217 A172218 A172219

Keyword

base,nonn

Author

Klaus Brockhaus, Jan 29 2010

Status

approved