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%I #27 Mar 21 2024 12:40:30
%S 7,23,113,2179,32749
%N Primes p such that between p and the next prime, 2 prime powers (A025475) occur.
%C No other terms < 4290000000. - _Jud McCranie_, Jun 20 2000
%C There are no other terms < 2^63. - _Donovan Johnson_, Mar 11 2013
%e Between 7 and 11 the 2 prime powers are 8 and 9, between 23 and 29 the 2 prime powers are 25 and 27, between 113 and 127 the 2 prime powers are 121 and 125, while between 32749 and 32771 the 2 prime powers are 32761 = 181^2 and 32768 = 2^15.
%t nn = 2^20; Prime /@ Keys@ Select[PositionIndex[PrimePi /@ Union@ Flatten@ Table[Array[p^# &, Floor@ Log[p, nn] - 1, 2], {p, Prime@ Range@ PrimePi@ Sqrt@ nn}]], Length[#] > 1 &] (* _Michael De Vlieger_, Mar 21 2024 *)
%o (PARI) isok(p) = isprime(p) && (q=nextprime(p+1)) && (v=vector(q-p, x, p+x)) && (#select(x->(isprimepower(x) && !isprime(x)), v) == 2);
%o lista(nn) = forprime(p=2, nn, if (isok(p), print1(p, ", "))); \\ _Michel Marcus_, Jul 15 2017
%Y Cf. A025475, A053607.
%K hard,more,nonn
%O 1,1
%A _Labos Elemer_, Feb 14 2000
%E Corrected by _James A. Sellers_, Feb 22 2000
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