A179839 -id:A179839 - cp's OEIS frontend

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

Juri-Stepan Gerasimov, Jan 10 2011

nonn

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

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

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

Cf. A001358, A001567.

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 *)

A176970 Numbers that are the product of two odd numbers x*y such that 2^x (mod y) = 2^y (mod x) = 2.

Original entry on oeis.org

9, 25, 49, 121, 169, 289, 341, 361, 525, 529, 651, 765, 841, 961, 1155, 1369, 1387, 1681, 1683, 1849, 1935, 2047, 2209, 2701, 2809, 3277, 3481, 3721, 3751, 4033, 4165, 4305, 4369, 4455, 4489, 4681, 5041, 5329, 5461, 5525, 5715, 6025, 6241, 6643, 6889, 7161, 7239, 7921, 7957, 8265, 8321, 8925, 9409, 9471, 9605

Offset: 1

Juri-Stepan Gerasimov, Jan 15 2011

nonn

The numbers that are the product of two such distinct odd numbers x*y are in A337715. - Bernard Schott, Oct 14 2020

			341 * 341 is a term because 2^341 mod 341 = 2.

Cf. A001567, A179707, A179839.

Cf. A337715 (subsequence).

okQ[x_,y_] := PowerMod[2, x, y] == PowerMod[2, y, x] == 2; n =10000; Union[Reap[Do[If[i*j < nn && okQ[i, j], Sow[i*j]], {i, 1, nn/3, 2}, {j, i, nn/3, 2}]][[2, 1]]] (* Harvey P. Dale, Jan 21 2011 *)

isok(n) = {if ((n % 2), fordiv(n, d, if ((d >= n/d) && (lift(Mod(2, d)^(n/d)) == 2) && (lift(Mod(2, n/d)^d) == 2), return(1));););} \\ Michel Marcus, Sep 17 2020

Definition clarified by T. D. Noe, Jan 17 2011

Corrected and extended by Harvey P. Dale, Jan 21 2011

cp's OEIS Frontend

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

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