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 1-4 of 4 results.

A334034 a(n) is the least integer that can be expressed as the difference of two pentagonal numbers in exactly n ways.

Original entry on oeis.org

1, 22, 70, 715, 1330, 4025, 6370, 14014, 17290, 25025, 45815, 73150, 121030, 95095, 85085, 256025, 350350, 432250, 1179178, 425425, 575575, 734825, 950950, 1926925, 3751930, 2187185, 1616615, 1956955, 3148145, 3658655, 4029025, 2977975, 4352425, 6656650, 13918450
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 12 2020

Keywords

Comments

The least integer that can be expressed as the sum of one or more consecutive numbers congruent to 1 mod 3 in exactly n ways.
Index of first occurrence of n in A333815.

Links

Crossrefs

Cf. A000326, A016777, A038547, A068314, A333815, A334008, A334035, A334036, A334037.

Extensions

More terms from Jinyuan Wang, Apr 13 2020

A334035 a(n) is the least integer that can be expressed as the difference of two hexagonal numbers in exactly n ways.

Original entry on oeis.org

1, 45, 225, 585, 2415, 4725, 9945, 10395, 31185, 28665, 45045, 58905, 143325, 257985, 135135, 225225, 329175, 487305, 405405, 831285, 1091475, 675675, 1396395, 1576575, 2927925, 3132675, 2436525, 2027025, 2567565, 2297295, 6235515, 5360355, 4729725, 3828825, 10503675
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 12 2020

Keywords

Comments

The least integer that can be expressed as the sum of one or more consecutive numbers congruent to 1 mod 4 in exactly n ways.
Index of first occurrence of n in A333816.

Links

Crossrefs

Cf. A000384, A016813, A038547, A068314, A333816, A334010, A334034, A334036, A334037.

Programs

  • Mathematica
    nmax = 10000; A333816 = Rest[CoefficientList[Series[Sum[x^(k*(2*k - 1))/(1 - x^(4*k)), {k, 1, 1 + Sqrt[nmax/2]}], {x, 0, nmax}], x]]; Flatten[Table[FirstPosition[A333816, k], {k, 1, Max[A333816]}]] (* Vaclav Kotesovec, Apr 19 2020 *)

Extensions

More terms from Jinyuan Wang, Apr 13 2020

A334037 a(n) is the least integer that can be expressed as the difference of two octagonal numbers in exactly n ways.

Original entry on oeis.org

1, 133, 560, 1729, 4160, 10640, 14560, 22400, 44800, 58240, 138320, 98560, 123200, 203840, 246400, 394240, 320320, 492800, 800800, 640640, 1047200, 1823360, 1724800, 1281280, 2094400, 1601600, 2475200, 2722720, 4484480, 3203200, 5532800, 6697600, 5445440, 7958720
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 12 2020

Keywords

Comments

The least integer that can be expressed as the sum of one or more consecutive numbers congruent to 1 mod 6 in exactly n ways.
Index of first occurrence of n in A333818.

Links

Crossrefs

Cf. A000567, A016921, A038547, A068314, A333818, A334012, A334034, A334035, A334036.

Extensions

More terms from Jinyuan Wang, Apr 13 2020

A338105 a(n) is the least integer that can be expressed as the difference of two n-gonal numbers in exactly n ways.

Original entry on oeis.org

9, 96, 1330, 4725, 21021, 22400, 421515, 675675, 5370365, 576576, 10790325, 39255125, 51548805, 7286400, 978624647, 144729585, 649593945, 125245120, 1109593485, 4519064403, 13908638315, 253955520, 8860666815, 30587913125, 33144736086, 859541760, 147839441750
Offset: 3

Views

Author

Ilya Gutkovskiy, Oct 10 2020

Keywords

Comments

a(17) <= 1340770739, a(18) = 144729585, a(19) <= 9381302307, a(20) <= 1257818848, a(21) <= 6299438145, a(22) <= 32911706919, a(23) <= 26720105555, a(24) <= 3141537984, a(25) <= 59558175105, a(26) <= 71119743695, a(27) <= 260207700831, a(28) <= 28582652736, a(29) <= 688883385190, a(30) <= 593086020813. - Chai Wah Wu, Oct 14 2020

Examples

			a(3) = 9 because 9 = 10 - 1 = 15 - 6 = 45 - 36 and this is the least integer that can be expressed as the difference of two triangular numbers in exactly 3 ways.

Links

Crossrefs

Cf. A038547, A068314, A072502, A257411, A334034, A334035, A334036, A334037.

Extensions

a(11)-a(16) from Chai Wah Wu, Oct 13 2020
a(17) and a(19)-a(40) from Martin Ehrenstein, Oct 23 2020
Showing 1-4 of 4 results.

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