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 A269769 Numbers of the form p^k - k where p is a prime number and k > 1. 2
 2, 5, 7, 12, 23, 24, 27, 47, 58, 77, 119, 121, 122, 167, 238, 248, 287, 340, 359, 503, 527, 621, 723, 839, 959, 1014, 1328, 1367, 1679, 1847, 2037, 2180, 2194, 2207, 2397, 2807, 3120, 3479, 3719, 4084, 4487, 4910, 5039, 5327, 6239, 6553, 6856, 6887, 7919, 8179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes of the form p^k - k where p is prime are 2, 5, 7, 23, 47, 167, 359, 503, ... Subsequence of A057897. A182474 is a subsequence. Up to 10^14 all the terms have a unique representation as p^k - k. - Giovanni Resta, Mar 21 2017 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 2 is a term because   2 = 2^2 - 2.     5 is a term because   5 = 2^3 - 3.     7 is a term because   7 = 3^2 - 2.    12 is a term because  12 = 2^4 - 4.   121 is a term because 121 = 2^7 - 7. MAPLE N:= 10000: # to get all terms <= N P:= select(isprime, [\$1..floor((N+2)^(1/2))]): S:= {}: for k from 2 do   pmax:= floor((N+k)^(1/k));   if pmax < 2 then break fi;   S:= S union {seq(p^k-k, p = select(`<=`, P, pmax))}; od: sort(convert(S, list)); # Robert Israel, Mar 21 2017 CROSSREFS Cf. A000961, A057897, A182474. Sequence in context: A333068 A029938 A213044 * A230428 A071013 A114727 Adjacent sequences:  A269766 A269767 A269768 * A269770 A269771 A269772 KEYWORD nonn AUTHOR Altug Alkan, Mar 04 2016 STATUS approved

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Last modified July 1 09:39 EDT 2022. Contains 354958 sequences. (Running on oeis4.)