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

Author

Juri-Stepan Gerasimov, Jan 10 2011

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A001358, A001567.

Programs

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 *)