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
Examples
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)
Links
- Eric Weisstein's World of Mathematics, Polygonal Number
Extensions
a(6)-a(9) from Michael S. Branicky, Feb 19 2023