A298427 -id:A298427 - cp's OEIS frontend

A298428 Numbers n such that there are precisely 10 groups of orders n and n + 1.

13914, 15974, 77234, 99126, 107205, 122675, 128894, 187473, 188265, 204134

Offset: 1

Muniru A Asiru, Jan 19 2018

Equivalently, lower member of consecutive terms of A249553.

			For n = 13914, A000001(13914) = A000001(13915) = 10.
For n = 15974, A000001(15974) = A000001(15975) = 10.
For n = 77234, A000001(77234) = A000001(77235) = 10.

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 A249553 (Numbers n having precisely 10 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), this sequence (k=10), A295994 (k=11), A295995 (k=15).

with(GroupTheory): for n from 1 to 10^5 do if [NumGroups(n), NumGroups(n+1)] = [10, 10] then print(n); fi; od;

Sequence is { n | A000001(n) = 10, A000001(n+1) = 10 }.

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

Original entry on oeis.org

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 }.

A298431 Numbers n such that there are precisely 14 groups of orders n and n + 1.

Original entry on oeis.org

4328, 22311, 29864, 57896, 75368, 99368, 120807, 130664, 131943, 152295, 157287, 164072, 180327, 184232, 212456, 236583, 268712, 276392, 331112, 338792, 381927

Offset: 1

Muniru A Asiru, Jan 19 2018

Equivalently, lower member of consecutive terms of A294155.

			For n = 4328, A000001(4328) = A000001(4329) = 14.
For n = 22311, A000001(22311) = A000001(22312) = 14.
For n = 29864, A000001(29864) = A000001(29865) = 14.

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 A294155 (Numbers n having precisely 14 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), this sequence (k=14), A295995 (k=15).

with(GroupTheory): for n from 1 to 10^5 do if [NumGroups(n), NumGroups(n+1)] = [14, 14] then print(n); fi; od;

Sequence is { n | A000001(n) = 14, A000001(n+1) = 14 }.

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 }.

A298912 Numbers n such that the number of groups of order n equals the number of groups of order n + 1.

Original entry on oeis.org

1, 2, 9, 21, 25, 38, 45, 57, 93, 105, 121, 165, 194, 201, 202, 205, 206, 218, 253, 261, 301, 315, 325, 326, 357, 361, 381, 385, 422, 453, 477, 482, 494, 506, 538, 542, 554, 603, 614, 626, 633, 662, 746, 758, 765, 801, 841, 861, 873, 897, 921, 925, 934, 1005, 1017

Offset: 1

Muniru A Asiru, Jan 28 2018

nonn

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. 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), A (k=10), A295994 (k=11), A295995 (k=15).

Filtered([1..500], n -> NumberSmallGroups(n) = NumberSmallGroups(n+1));

with(GroupTheory):
for n from 1 to 300 do if NumGroups(n+1) = NumGroups(n) then print(n); fi; od;

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

cp's OEIS Frontend

A298428 Numbers n such that there are precisely 10 groups of orders n and n + 1.

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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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A298431 Numbers n such that there are precisely 14 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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A298912 Numbers n such that the number of groups of order n equals the number of groups of order n + 1.

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