A053704 -id:A053704 - cp's OEIS frontend

A053702 Odd prime powers p^w (w>1) such that p^w+2 is prime.

9, 27, 81, 125, 6561, 24389, 59049, 161051, 357911, 571787, 1442897, 4782969, 5177717, 14348907, 18191447, 30080231, 73560059, 80062991, 118370771, 127263527, 131872229, 318611987, 344472101, 440711081, 461889917, 590589719, 756058031, 865523177

Offset: 1

Labos Elemer, Feb 14 2000

nonn

			Examples: powers of 3 like 9,27,81,6561,59049; powers of 5 like 125; others like 23^3=24389, 71^3=357911, 83^3=571787, 11^5=161051, ...

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A025475, A053704.

Table[Do[s=2+Prime[w]^n; If[PrimeQ[s]&&!Greater[s, 10000000000], Print[s]], {n, 2, 35}], {w, 1, 1000}]

A025475(n)+2 is prime

A053705 Primes p of form q^k-2 where q is also a prime and k > 1.

Original entry on oeis.org

2, 7, 23, 47, 79, 167, 241, 359, 727, 839, 1367, 1847, 2207, 2399, 3719, 5039, 6857, 7919, 10607, 11447, 14639, 16127, 17159, 19319, 19681, 28559, 29789, 29927, 36479, 44519, 49727, 50651, 54287, 57119, 66047, 85847, 97967, 113567, 128879

Offset: 1

Labos Elemer, Feb 14 2000

nonn

			79 = 3^4-2.
241 = 3^5-2.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A025475, A053704.

Subsequence of A267944.

Do[s=2+Prime[n]; If[Equal[Length[FactorInteger[s]], 1]&&!PrimeQ[s], Print[s-2]], {n, 1, 100000}]
fQ[n_] := PrimeNu[n + 2] == 1 && ! PrimeQ[n + 2]; Select[ Prime@ Range@ 15000, fQ] (* Robert G. Wilson v, Apr 01 2012 *)
seq[max_] := Module[{s = {}, p = 2}, While[p^2 <= max, s = Join[s, Select[p^Range[2, Floor[Log[p, max]]], PrimeQ[# - 2] &]]; p = NextPrime[p]]; Union[s] - 2]; seq[150000] (* Amiram Eldar, Aug 27 2024 *)

lista(nn) = forprime (p=1, nn, if (ispower(p+2,,&q) && isprime(q), print1(p, ", ")); ); \\ Michel Marcus, Dec 11 2014

a(n) = A053704(n) - 2. - Amiram Eldar, Aug 27 2024

Definition corrected by Zak Seidov, Dec 11 2014

cp's OEIS Frontend

A053702 Odd prime powers p^w (w>1) such that p^w+2 is prime.

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