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%I #20 Apr 12 2016 09:50:53
%S 1,2,3,8,9,25,32,512,6561,36703368217294125441230211032033660188801
%N 1 and the prime powers (p^k, p prime, k >= 1) such that p^k - k and p^k + k are prime powers.
%C a(10) = 7^48. If it exists, a(11) > 10^100. - _Giovanni Resta_, Apr 12 2016
%e 6561 is in this sequence because 6561 = 3^8, 6561 - 8 = 6553 is prime and 6561 + 8 = 6569 is prime.
%t nn = 10^6; {1}~Join~Sort@ Apply[Power, Select[Flatten[Function[k, {#, k}] /@ Range[Floor@ Log[#, nn]] & /@ Prime@ Range@ PrimePi@ nn, 1], With[{p = First@ #, k = Last@ #}, And[Or[PrimePowerQ@ #, # == 1] &[p^k - k], Or[PrimePowerQ@ #, # == 1] &[p^k + k]]] &], 1] (* _Michael De Vlieger_, Apr 06 2016 *)
%o (PARI) ispp(n) = (n==1) || isprimepower(n);
%o isok(n) = (n==1) || ((k=isprimepower(n)) && ispp(n+k) && ispp(n-k));
%o \\ _Michel Marcus_, Apr 07 2016
%Y Cf. A000961, A025474.
%K nonn,more
%O 1,2
%A _Juri-Stepan Gerasimov_, Apr 06 2016
%E a(10) from _Giovanni Resta_, Apr 12 2016
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