A179707 Semiprimes p*q such that 2^p (mod q) == 2^q (mod p).

4, 9, 25, 49, 121, 169, 289, 341, 361, 529, 731, 841, 961, 1333, 1369, 1387, 1681, 1727, 1849, 2047, 2209, 2701, 2809, 3277, 3481, 3503, 3721, 3763, 4033, 4369, 4489, 4681, 5041, 5329, 5461, 6241, 6889, 7921, 7957, 8321, 9409, 9509, 10201, 10261, 10609, 10669, 11449, 11881

Offset

1,1

Comments

The square of every prime is here, as are the semiprimes in A179839.

Links

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

Example

341 is a term because 341=11*31 and 2^11 mod 31 = 2^31 mod 11.

Mathematica

fQ[n_] := Block[{fi = Flatten[ Table[ First@ #, {Last@ #}] & /@ FactorInteger@ n]}, Length@ fi == 2 && PowerMod[2, fi[[2]], fi[[1]]] == PowerMod[2, fi[[1]], fi[[2]]]]; Select[ Range@ 12000, fQ]
With[{nn=50}, Take[Union[Times@@@Select[Tuples[Prime[Range[2nn]], 2], PowerMod[ 2, #[[1]], #[[2]]]==PowerMod[2, #[[2]], #[[1]]]&]], nn]] (* Harvey P. Dale, Sep 03 2015 *)

Crossrefs

Cf. A001358, A001567.

Sequence in context: A082180 A246131 A068999 * A247078 A077438 A350343

Adjacent sequences: A179704 A179705 A179706 * A179708 A179709 A179710

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 10 2011

Status

approved