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A053706
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Primes p such that between p and the next prime, 2 prime powers (A025475) occur.
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1
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(PARI) isok(p) = isprime(p) && (q=nextprime(p+1)) && (v=vector(q-p, x, p+x)) && (#select(x->(isprimepower(x) && !isprime(x)), v) == 2);
lista(nn) = forprime(p=2, nn, if (isok(p), print1(p, ", "))); \\ Michel Marcus, Jul 15 2017
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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