A131748 Minimum prime that raised to the powers from 1 to n produces numbers whose sums of digits are also primes.

2, 5, 739, 47, 4229, 2803, 27617, 142589, 108271, 2347283, 1108739, 300776929, 300776929, 14674550173, 92799126239

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Example

n=3 -> 739:
739^1 = 739 Sum_digits(739) = 19 which is prime;
739^2 = 546121 Sum_digits(546121) = 19 which is prime;
739^3 = 403583419 Sum_digits(403583419) = 37 which is prime;
n=5 -> p=4229:
4229^1 = 4229 Sum_digits(4229) = 17 which is prime;
4229^2 = 17884441 Sum_digits(17884441) = 37 which is prime
4229^3 = 75633300989 Sum_digits(75633300989) = 53 which is prime
4229^4 = 319853229882481 Sum_digits(319853229882481) = 73 which is prime
4229^5 = 1352659309173012149 Sum_digits(1352659309173012149) = 71 which is prime

Maple

P:=proc(n, m) local cont, i, k, w, ok; ok:=true; i:=0; while ok do i:=i+1; cont:=0; w:=i; if isprime(i) then while cont<50 and isprime(w) do cont:=cont+1; w:=0; k:=i^cont; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; od; if (cont-1)=m then lprint(i, cont-1); ok:=false; fi; fi; od; end: P(10000000, 11);

Crossrefs

Cf. A046704.

Sequence in context: A068105 A065588 A208277 * A240768 A212590 A208212

Adjacent sequences: A131745 A131746 A131747 * A131749 A131750 A131751

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 29 2007

Extensions

a(12)-a(13) from Charles R Greathouse IV, Nov 18 2010

a(14)-a(15) from Charles R Greathouse IV, Mar 09 2011

Status

approved