A273179 Numbers k for which 2 has exactly four square roots mod k.

119, 161, 217, 238, 287, 322, 329, 391, 434, 497, 511, 527, 553, 574, 623, 658, 679, 697, 713, 721, 782, 791, 799, 833, 889, 943, 959, 994, 1022, 1054, 1057, 1081, 1106, 1127, 1169, 1207, 1241, 1246, 1271, 1337, 1343, 1351, 1358, 1393, 1394, 1426, 1442, 1457, 1513

Offset: 1

Author

Dale Taylor, May 17 2016

Keywords

• nonn

Comments

Sequence is fairly regular; 437 numbers below 1000 have 4 square roots of 2 mod k; 4796 below 10^4; 47276 below 10^5; and 452172 below 10^6.

Examples

			2 has square roots 11, 45, 74, 108 mod 119; e.g., 11^2 == 2 (mod 119).
		

Crossrefs

Subsequence of A057126 (Numbers n such that 2 is a square mod n).

Programs

Mathematica

Select[Range[3000], Length@PowerModList[2, 1/2, #] == 4 &]