A296026 Numbers n such that there are precisely 2 groups of order n and 4 of order n + 1.

62, 129, 153, 169, 237, 245, 274, 278, 285, 289, 314, 369, 386, 417, 425, 429, 497, 529, 555, 597, 637, 645, 669, 715, 813, 889, 914, 926, 955, 961, 969, 1065, 1101, 1131, 1154, 1221, 1227, 1286, 1341, 1369, 1389, 1405, 1435, 1461, 1497, 1505, 1515, 1557, 1569, 1675, 1771

Offset

1,1

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1241

H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.

Gordon Royle, Numbers of Small Groups

Index entries for sequences related to groups

Formula

Sequence is { n | A000001(n) = 2, A000001(n+1) = 4 }.

Example

62 is in the sequence since A000001(62) = 2 and A000001(63) = 4.
129 is in the sequence since A000001(129) = 2 and A000001(130) = 4.
425 is in the sequence since A000001(425) = 2 and A000001(426) = 4.

Maple

with(GroupTheory):
for n from 1 to 10^3 do if [NumGroups(n), NumGroups(n+1)]=[2, 4]  then print(n); fi; od;

Prog

(GAP) A296026 := Filtered([1..2014], n->[NumberSmallGroups(n), NumberSmallGroups(n+1)]=[2, 4]);

Crossrefs

Cf. A000001. Subsequence of A054395.

Sequence in context: A044249 A044630 A103584 * A107581 A259738 A367092

Adjacent sequences: A296023 A296024 A296025 * A296027 A296028 A296029

Keyword

nonn

Author

Muniru A Asiru, Dec 03 2017

Status

approved