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

1,1

Comments

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

Links

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

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 *)

Crossrefs

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

Sequence in context: A321868 A175736 A372896 * A172255 A087835 A271221

Adjacent sequences: A179836 A179837 A179838 * A179840 A179841 A179842

Keyword

nonn

Author

T. D. Noe, Jan 10 2011

Status

approved