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

1,1

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.

Links

Table of n, a(n) for n=1..49.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A333789 A135716 A026049 * A247137 A134603 A134604

Adjacent sequences: A273176 A273177 A273178 * A273180 A273181 A273182

Keyword

nonn

Author

Dale Taylor, May 17 2016

Status

approved