A242368 Primes p such that p + digitsum(p) = q^k for some prime q and k > 1 where digitsum(n) = A007953(n).

2, 17, 347, 521, 10601, 28541, 29759, 32027, 39569, 58061, 62969, 100469, 109541, 120401, 130307, 205357, 398129, 426383, 434261, 829883, 896771, 923501, 935063, 1190261, 1216583, 1261109, 1559963, 1697771, 2105381, 2128649, 2505857, 2778851, 2886563, 2920649

Offset: 1

Author

J. M. Bergot, Aug 16 2014

Keywords

• nonn
• base

Comments

With k>1 the number of entries is greatly reduced compared to simply allowing p+digsum(p) = q. One could allow for k=1 to see how many entries could be found for a variation of this sequence.

Examples

			a(4)=521 because 521+5+2+1=529=23^2 and 23 is a prime.
		

Links

• Kevin P. Thompson, Table of n, a(n) for n = 1..1000 (first 181 terms from Michel Marcus)

Crossrefs

Cf. A000040, A007953, A007605, A000961.

Programs

Mathematica

a242368[n_Integer] := Module[{p, pp}, p = Prime[n]; pp = p + Plus @@ IntegerDigits@p; If[And[Length@FactorInteger[pp] == 1,
    Min[Last@Transpose[FactorInteger[pp]]] > 1], p, 0]]; Rest@Sort@DeleteDuplicates[a242368 /@ Range[10^6]] (* Michael De Vlieger, Aug 16 2014 *)

PARI

dsum(n)=n=digits(n); sum(i=1,#n,n[i])
is(p)=isprimepower(p+dsum(p))>1 && isprime(p)
forprime(p=2,1e9,if(is(p), print1(p", "))) \\ Charles R Greathouse IV, Aug 16 2014

Extensions

More terms from Charles R Greathouse IV, Aug 16 2014