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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.

%I A360762 #22 Feb 16 2025 08:34:04
%S A360762 9,12880,20449,10764222,794629045,33205080888,5985,13925100
%N 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.
%H A360762 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%e A360762 For n = 2: 9 = 2 + 3 + 4 = 4 + 5.
%e A360762 For n = 3: 12880 = 91 + ... + 903 = 300 + ... + 990.
%e A360762 For n = 4: 20449 = 7^2 + ... + 39^2 = 38^2 + ... + 48^2.
%e A360762 For n = 5: 10764222 = 1617 + ... + 115787 = 31032 + ... + 126005.
%e A360762 From _Michael S. Branicky_, Feb 19 2023: (Start)
%e A360762 n-th term and indices of n-gonal numbers summing to it:
%e A360762 a(2) = 9: 2..4, 4..5,
%e A360762 a(3) = 12880: 13..42, 24..44,
%e A360762 a(4) = 20449: 7..39, 38..48,
%e A360762 a(5) = 10764222: 33..278, 144..290,
%e A360762 a(6) = 794629045: 1305..1505, 5321..5334,
%e A360762 a(7) = 33205080888: 616..3422, 3235..4192,
%e A360762 a(8) = 5985: 1..18, 11..19,
%e A360762 a(9) = 13925100: 103..235, 220..282. (End)
%Y A360762 Cf. A057145, A062681, A307608, A307614, A343777, A360777.
%K A360762 nonn,more
%O A360762 2,1
%A A360762 _Ilya Gutkovskiy_, Feb 19 2023
%E A360762 a(6)-a(9) from _Michael S. Branicky_, Feb 19 2023