A068314 -id:A068314 - cp's OEIS frontend

A334036 a(n) is the least integer that can be expressed as the difference of two heptagonal numbers in exactly n ways.

1, 81, 468, 1911, 6237, 11781, 21021, 51051, 81081, 121737, 261261, 318087, 513513, 671517, 1145529, 1072071, 1582581, 1378377, 3216213, 2513511, 4135131, 4700619, 5666661, 11792781, 8729721, 11810799, 15444891, 19270251, 15162147, 24657633, 28945917, 26189163

Offset: 1

Ilya Gutkovskiy, Apr 12 2020

nonn

The least integer that can be expressed as the sum of one or more consecutive numbers congruent to 1 mod 5 in exactly n ways.

Index of first occurrence of n in A333817.

Eric Weisstein's World of Mathematics, Heptagonal Number
Index to sequences related to polygonal numbers

Cf. A000566, A016861, A038547, A068314, A333817, A334011, A334034, A334035, A334037.

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

Ilya Gutkovskiy, Oct 10 2020

nonn

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

			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.

Martin Ehrenstein, Table of n, a(n) for n = 3..40
Eric Weisstein's World of Mathematics, Polygonal Number
Index to sequences related to polygonal numbers

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

a(11)-a(16) from Chai Wah Wu, Oct 13 2020

a(17) and a(19)-a(40) from Martin Ehrenstein, Oct 23 2020

A368041 a(n) is the least number k such that k^2 can be written as the difference of two positive squares in exactly n ways.

Original entry on oeis.org

1, 3, 8, 16, 12, 64, 128, 24, 512, 1024, 48, 4096, 72, 60, 32768, 65536, 192, 144, 524288, 384, 2097152, 4194304, 120, 16777216, 432, 1536, 134217728, 576, 3072, 1073741824, 2147483648, 240, 1152, 17179869184, 12288, 68719476736, 137438953472, 360, 1728, 1099511627776

Offset: 0

Ilya Gutkovskiy, Dec 09 2023

nonn

Index of first occurrence of n in A046079.

All the terms are of the form 2^m * A147516(k), m >= 0, k >= 1. - Amiram Eldar, Nov 08 2024

			a(2) = 8: 8^2 = 10^2 - 6^2 = 17^2 - 15^2.

Amiram Eldar, Table of n, a(n) for n = 0..999

Cf. A025487, A046079, A068314, A071571, A094191, A100073, A122842, A147516.

a(n) = min(A122842(n+1), 2*A071571(n)). - Jon E. Schoenfield, Dec 09 2023

a(26)-a(29) from Michel Marcus, Dec 09 2023

a(30)-a(39) from Jon E. Schoenfield, Dec 09 2023

A334078 a(n) is the smallest positive integer that can be expressed as the difference of two positive squares in at least n ways.

Original entry on oeis.org

3, 15, 45, 96, 192, 240, 480, 480, 720, 960, 1440, 1440, 2880, 2880, 2880, 3360, 5040, 5040, 6720, 6720, 10080, 10080, 10080, 10080, 20160, 20160, 20160, 20160, 20160, 20160, 30240, 30240, 40320, 40320, 40320, 40320, 60480, 60480, 60480, 60480, 80640, 80640

Offset: 1

Ilya Gutkovskiy, Apr 13 2020

nonn

Eric Weisstein's World of Mathematics, Square Number

Cf. A000290, A024352, A048610, A068314, A094191, A100073, A214771, A334077.

A329236 a(n) is the least integer that can be expressed as the sum of one or more consecutive centered triangular numbers in exactly n ways.

Original entry on oeis.org

1, 64, 1789760

Offset: 1

Ilya Gutkovskiy, Apr 13 2020

If it exists, a(4) > 10^18. - Bert Dobbelaere, Apr 17 2020

Eric Weisstein's World of Mathematics, Centered Triangular Number

Cf. A005448, A054859, A068314, A298467, A322610, A334007.

cp's OEIS Frontend

A334036 a(n) is the least integer that can be expressed as the difference of two heptagonal numbers in exactly n ways.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A368041 a(n) is the least number k such that k^2 can be written as the difference of two positive squares in exactly n ways.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

Extensions

A334078 a(n) is the smallest positive integer that can be expressed as the difference of two positive squares in at least n ways.

Views

Author

Keywords

Links

Crossrefs

A329236 a(n) is the least integer that can be expressed as the sum of one or more consecutive centered triangular numbers in exactly n ways.

Views

Author

Keywords

Comments

Links

Crossrefs