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

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

Author

Juri-Stepan Gerasimov, Jan 15 2011

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A001567, A179707, A179839.

Cf. A337715 (subsequence).

Programs

Mathematica

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 *)

PARI

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

Extensions

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

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