cp's OEIS Frontend

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

%I A076705 #8 Apr 06 2020 12:31:29
%S A076705 4,8,9,27,121,125,243,1331,4489,10201,12769,24649,37249,66049,80089,
%T A076705 96721,113569,139129,167281,175561,177147,214369,259081,358801,371293,
%U A076705 413449,426409,436921,552049,579121,591361,635209,823543,1026169
%N A076705 Prime powers of prime numbers such that the sum of its digits is also prime power of prime number.
%C A076705 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.
%H A076705 Robert Israel, <a href="/A076705/b076705.txt">Table of n, a(n) for n = 1..10000</a>
%p A076705 N:= 2000000: # for terms <= N
%p A076705 R:= NULL:
%p A076705 p:= 1:
%p A076705 do
%p A076705   p:= nextprime(p);
%p A076705   if p^2 > N then break fi;
%p A076705   q:= 1;
%p A076705   do
%p A076705     q:= nextprime(q);
%p A076705     x:= p^q;
%p A076705     if x > N then break fi;
%p A076705     R:= R, x;
%p A076705   od;
%p A076705 od:
%p A076705 S:= {R}:
%p A076705 sort(convert(select(s -> member(convert(convert(s,base,10),`+`),S),S), list));  # _Robert Israel_, Apr 06 2020
%t A076705 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}]
%Y A076705 Cf. A053810, A075308.
%K A076705 nonn,base
%O A076705 1,1
%A A076705 _Zak Seidov_, Oct 26 2002
%E A076705 Edited and corrected by _Robert G. Wilson v_, Oct 31 2002