A076705 Prime powers of prime numbers such that the sum of its digits is also prime power of prime number.

4, 8, 9, 27, 121, 125, 243, 1331, 4489, 10201, 12769, 24649, 37249, 66049, 80089, 96721, 113569, 139129, 167281, 175561, 177147, 214369, 259081, 358801, 371293, 413449, 426409, 436921, 552049, 579121, 591361, 635209, 823543, 1026169

Offset: 1

Author

Zak Seidov, Oct 26 2002

Keywords

• nonn
• base

Comments

Up to 10^7, there are 513 prime powers of prime numbers. Of these, 79 are such that the sum of their digits is also prime power of prime number. Up to 10^14 there are 43915.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053810, A075308.

Programs

Maple

N:= 2000000: # for terms <= N
R:= NULL:
p:= 1:
do
  p:= nextprime(p);
  if p^2 > N then break fi;
  q:= 1;
  do
    q:= nextprime(q);
    x:= p^q;
    if x > N then break fi;
    R:= R, x;
  od;
od:
S:= {R}:
sort(convert(select(s -> member(convert(convert(s,base,10),`+`),S),S), list));  # Robert Israel, Apr 06 2020

Mathematica

pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^14]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^14]]]}]]]; a = {}; Do[ If[ Position[pp, Plus @@ IntegerDigits[ pp[[n]] ]] != {}, a = Append[a, pp[[n]] ]], {n, 1, 669541}]

Extensions

Edited and corrected by Robert G. Wilson v, Oct 31 2002