A134535 Numbers n such that the sum of the digits of 13^n is prime.

3, 6, 10, 14, 15, 24, 30, 33, 34, 39, 40, 47, 53, 57, 61, 71, 75, 76, 80, 81, 83, 88, 89, 92, 102, 103, 106, 117, 131, 143, 144, 147, 154, 163, 170, 187, 198, 200, 205, 210, 212, 221, 227, 238, 240, 253, 255, 260, 262, 265, 271, 275

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 30 2007

Keywords

• easy
• nonn
• base

Examples

			13^3=2197 and 2+1+9+7=19 is prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A076203, A134532, A134533, A134534.

Programs

Maple

P:=proc(n) local cont,i,k,w; if isprime(n) then cont:=0; while cont<1000 do cont:=cont+1; w:=0; k:=n^cont; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if isprime(w) then print(cont); fi; od; fi; end: P(13);

Mathematica

Select[Range[250], PrimeQ[Total[IntegerDigits[13^#]]]&] (* Vincenzo Librandi, Apr 17 2013 *)