cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A298427 Numbers n such that there are precisely 9 groups of orders n and n + 1.

Original entry on oeis.org

38227, 113476, 155827, 269444, 336931, 411747
Offset: 1

Views

Author

Muniru A Asiru, Jan 19 2018

Keywords

Comments

Equivalently, lower member of consecutive terms of A249552.

Examples

			For n = 38227, A000001(38227) = A000001(38228) = 9.
For n = 113476, A000001(113476) = A000001(113477) = 9.
For n = 155827, A000001(155827) = A000001(155828) = 9.

Links

Crossrefs

Cf. A000001. Subsequence of A249552 (Numbers n having precisely 9 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), this sequence (k=9), A298428 (k=10), A295994 (k=11), A295995 (k=15).

Programs

  • Maple
    with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [9, 9] then print(n); fi; od;

Formula

Sequence is { n | [A000001(n), A000001(n+1)] = [9, 9] }.

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

Original entry on oeis.org

13914, 15974, 77234, 99126, 107205, 122675, 128894, 187473, 188265, 204134
Offset: 1

Views

Author

Muniru A Asiru, Jan 19 2018

Keywords

Comments

Equivalently, lower member of consecutive terms of A249553.

Examples

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

Links

Crossrefs

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).

Programs

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

Formula

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

Views

Author

Muniru A Asiru, Jan 19 2018

Keywords

Comments

Equivalently, lower member of consecutive terms of A249555.

Examples

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

Links

Crossrefs

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).

Programs

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

Formula

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

Views

Author

Muniru A Asiru, Jan 19 2018

Keywords

Comments

Equivalently, lower member of consecutive terms of A292896.

Examples

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

Links

Crossrefs

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).

Programs

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

Formula

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

Views

Author

Muniru A Asiru, Jan 19 2018

Keywords

Comments

Equivalently, lower member of consecutive terms of A294155.

Examples

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

Links

Crossrefs

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).

Programs

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

Formula

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

Views

Author

Muniru A Asiru, Jan 19 2018

Keywords

Comments

Equivalently, lower member of consecutive terms of A295161.

Examples

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

Links

Crossrefs

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).

Programs

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

Formula

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

Views

Author

Muniru A Asiru, Jan 28 2018

Keywords

Links

Crossrefs

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).

Programs

  • GAP
    Filtered([1..500], n -> NumberSmallGroups(n) = NumberSmallGroups(n+1));
  • Maple
    with(GroupTheory):
for n from 1 to 300 do if NumGroups(n+1) = NumGroups(n) then print(n); fi; od;

Formula

Sequence is { n | A000001(n+1) = A000001(n) }.
Showing 1-7 of 7 results.

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