cp's OEIS Frontend

A269769 Numbers of the form p^k - k where p is a prime number and k > 1.

%I A269769 #21 Jan 20 2020 21:43:14
%S A269769 2,5,7,12,23,24,27,47,58,77,119,121,122,167,238,248,287,340,359,503,
%T A269769 527,621,723,839,959,1014,1328,1367,1679,1847,2037,2180,2194,2207,
%U A269769 2397,2807,3120,3479,3719,4084,4487,4910,5039,5327,6239,6553,6856,6887,7919,8179
%N A269769 Numbers of the form p^k - k where p is a prime number and k > 1.
%C A269769 Primes of the form p^k - k where p is prime are 2, 5, 7, 23, 47, 167, 359, 503, ...
%C A269769 Subsequence of A057897.
%C A269769 A182474 is a subsequence.
%C A269769 Up to 10^14 all the terms have a unique representation as p^k - k. - _Giovanni Resta_, Mar 21 2017
%H A269769 Robert Israel, <a href="/A269769/b269769.txt">Table of n, a(n) for n = 1..10000</a>
%e A269769     2 is a term because   2 = 2^2 - 2.
%e A269769     5 is a term because   5 = 2^3 - 3.
%e A269769     7 is a term because   7 = 3^2 - 2.
%e A269769    12 is a term because  12 = 2^4 - 4.
%e A269769   121 is a term because 121 = 2^7 - 7.
%p A269769 N:= 10000: # to get all terms <= N
%p A269769 P:= select(isprime, [$1..floor((N+2)^(1/2))]):
%p A269769 S:= {}:
%p A269769 for k from 2 do
%p A269769   pmax:= floor((N+k)^(1/k));
%p A269769   if pmax < 2 then break fi;
%p A269769   S:= S union {seq(p^k-k, p = select(`<=`,P,pmax))};
%p A269769 od:
%p A269769 sort(convert(S,list)); # _Robert Israel_, Mar 21 2017
%Y A269769 Cf. A000961, A057897, A182474.
%K A269769 nonn
%O A269769 1,1
%A A269769 _Altug Alkan_, Mar 04 2016