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

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

Author

Ilya Gutkovskiy, Oct 10 2020

Keywords

• nonn

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

• 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

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