login
a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero hexagonal numbers in exactly n ways.
6

%I #10 Feb 16 2025 08:34:00

%S 1,703,274550,11132303325

%N a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero hexagonal numbers in exactly n ways.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%e Let S(k, m) denote the sum of m hexagonal numbers starting from the k-th. We have

%e a(1) = S(1, 1);

%e a(2) = S(19, 1) = S(13, 2);

%e a(3) = S(62, 25) = S(184, 4) = S(25, 51);

%e a(4) = S(3065, 505) = S(22490, 11) = S(1215, 1430) = S(1938, 946).

%Y Cf. A000384, A054859, A068314, A186337, A298467, A319185, A334007, A334008, A334011, A334012.

%K nonn,hard,more,changed

%O 1,2

%A _Ilya Gutkovskiy_, Apr 12 2020

%E a(4) from _Giovanni Resta_, Apr 13 2020