A360762 a(n) is the least n-gonal number that is the sum of two or more consecutive nonzero n-gonal numbers in more than one way, or -1 if no such number exists.

9, 12880, 20449, 10764222, 794629045, 33205080888, 5985, 13925100

Offset

2,1

Links

Table of n, a(n) for n=2..9.

Eric Weisstein's World of Mathematics, Polygonal Number

Example

For n = 2: 9 = 2 + 3 + 4 = 4 + 5.
For n = 3: 12880 = 91 + ... + 903 = 300 + ... + 990.
For n = 4: 20449 = 7^2 + ... + 39^2 = 38^2 + ... + 48^2.
For n = 5: 10764222 = 1617 + ... + 115787 = 31032 + ... + 126005.
From Michael S. Branicky, Feb 19 2023: (Start)
n-th term and indices of n-gonal numbers summing to it:
a(2) = 9: 2..4, 4..5,
a(3) = 12880: 13..42, 24..44,
a(4) = 20449: 7..39, 38..48,
a(5) = 10764222: 33..278, 144..290,
a(6) = 794629045: 1305..1505, 5321..5334,
a(7) = 33205080888: 616..3422, 3235..4192,
a(8) = 5985: 1..18, 11..19,
a(9) = 13925100: 103..235, 220..282. (End)

Crossrefs

Cf. A057145, A062681, A307608, A307614, A343777, A360777.

Sequence in context: A055320 A271717 A069501 * A206461 A258719 A292562

Adjacent sequences: A360759 A360760 A360761 * A360763 A360764 A360765

Keyword

nonn,more

Author

Ilya Gutkovskiy, Feb 19 2023

Extensions

a(6)-a(9) from Michael S. Branicky, Feb 19 2023

Status

approved