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

1,1

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

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}]

Crossrefs

Cf. A053810, A075308.

Sequence in context: A075783 A098121 A115656 * A306916 A355063 A162752

Adjacent sequences: A076702 A076703 A076704 * A076706 A076707 A076708

Keyword

nonn,base

Author

Zak Seidov, Oct 26 2002

Extensions

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

Status

approved