A298431 -id:A298431 - cp's OEIS frontend

A298429 Numbers n such that there are precisely 12 groups of orders n and n + 1.

30135, 76312, 130890, 173445, 356610

Offset: 1

Muniru A Asiru, Jan 19 2018

Equivalently, lower member of consecutive terms of A249555.

			For n = 30135, A000001(30135) = A000001(30136) = 12.
For n = 76312, A000001(76312) = A000001(76313) = 12.
For n = 130890, A000001(130890) = A000001(130891) = 12.

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

Cf. A000001. Subsequence of A249555 (Numbers n having precisely 12 groups of order n). Numbers n having precisely k groups of orders n and n+1: A295230 (k=2), A295990 (k=4), A295991 (k=5), A295992 (k=6), A295993 (k=8), A298427 (k=9), A298428 (k=10), A295994 (k=11), this sequence (k=12), A298430 (k=13), A298431 (k=14), A295995 (k=15).

withGroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [12, 12] then print(n); fi; od;

Sequence is { n | A000001(n) = 12, A000001(n+1) = 12 }.

A298430 Numbers n such that there are precisely 13 groups of orders n and n + 1.

Original entry on oeis.org

82323, 390446, 622916, 774548, 793827, 876932

Offset: 1

Muniru A Asiru, Jan 19 2018

Equivalently, lower member of consecutive terms of A292896.

			For n = 82323, A000001(82323) = A000001(82324) = 13.
For n = 390446, A000001(390446) = A000001(390447) = 13.
For n = 622916, A000001(622916) = A000001(622917) = 13.

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

Cf. A000001. Subsequence of A292896 (Numbers n having precisely 13 groups of order n). Numbers n having precisely k groups of orders n and n+1: A295230 (k=2), A295990 (k=4), A295991 (k=5), A295992 (k=6), A295993 (k=8), A298427 (k=9), A298428 (k=10), A295994 (k=11), A298429 (k=12), this sequence (k=13), A298431 (k=14), A295995 (k=15).

with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [13, 13] then print(n); fi; od;

Sequence is { n | A000001(n) = 13, A000001(n+1) = 13 }.

A298437 Numbers n such that there are precisely 16 groups of orders n and n + 1.

Original entry on oeis.org

83132, 86049, 173529, 492830, 704241, 889406

Offset: 1

Muniru A Asiru, Jan 19 2018

Equivalently, lower member of consecutive terms of A295161.

			For n = 83132, A000001(83132) = A000001(83133) = 16.
For n = 173529, A000001(173529) = A000001(173530) = 16.
For n = 492830, A000001(492830) = A000001(492831) = 16.

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

Cf. A000001. Subsequence of A295161 (Numbers n having precisely 16 groups of order n). Numbers n having precisely k groups of orders n and n+1: A295230 (k=2), A295990 (k=4), A295991 (k=5), A295992 (k=6), A295993 (k=8), A298427 (k=9), A298428 (k=10), A295994 (k=11), A298429 (k=12), A298430 (k=13), A298431 (k=14), A295995 (k=15), this sequence (k=16).

with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [16, 16] then print(n); fi; od;

Sequence is { n | A000001(n) = 16, A000001(n+1) = 16 }.

cp's OEIS Frontend

A298429 Numbers n such that there are precisely 12 groups of orders n and n + 1.

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A298430 Numbers n such that there are precisely 13 groups of orders n and n + 1.

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A298437 Numbers n such that there are precisely 16 groups of orders n and n + 1.

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