A179839 Semiprimes p*q with p < q and 2^p (mod q) == 2^q (mod p).

341, 731, 1333, 1387, 1727, 2047, 2701, 3277, 3503, 3763, 4033, 4369, 4681, 5461, 7957, 8321, 9509, 10261, 10669, 13747, 14491, 15709, 17557, 17861, 18721, 19147, 19951, 20737, 23377, 31417, 31609, 31621, 35333, 42799, 43921, 44669, 46979, 49141, 49901, 49981

Offset: 1

Author

T. D. Noe, Jan 10 2011

Keywords

• nonn

Comments

The semiprime super-Poulet numbers (semiprimes in A050217) are a subsequence.

Links

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

Crossrefs

Cf. A006881, A179707 (which allows p = q).

Programs

Mathematica

aQ[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 2 && f[[1, 2]] == f[[2, 2]] == 1, p = f[[1, 1]]; q = f[[2, 1]], Return[False]]; PowerMod[2, p, q] == PowerMod[2, q, p]]; Select[Range[50000], aQ] (* Amiram Eldar, Oct 23 2019 *)
Take[Times@@@Select[Tuples[Prime[Range[350]],2],#[[1]]!=#[[2]]&&PowerMod[2,#[[1]],#[[2]]]==PowerMod[2,#[[2]],#[[1]]]&]//Union,40] (* Harvey P. Dale, Jun 06 2025 *)