A359317 a(n) is the smallest tetrahedral number with binary weight n.

0, 1, 10, 35, 120, 220, 455, 2024, 1771, 4060, 14190, 16215, 129766, 32509, 1414910, 1823471, 5159805, 8171255, 4192244, 24117100, 30865405, 334985911, 192937325, 1610599145, 1048440315, 4261347265, 4244012991, 63828916911, 213588635511, 133110357279

Offset: 0

Author

Ilya Gutkovskiy, Dec 25 2022

Keywords

• nonn
• base

Examples

			455 is the smallest tetrahedral number with binary weight 6 (455_10 = 111000111_2), so a(6) = 455.
		

Links

• Eric Weisstein's World of Mathematics, Tetrahedral Number
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A000292, A089999, A358931, A359318.

Programs

Mathematica

seq[len_,nmax_] := Module[{s = Table[0,{len}], n = 0, c = 0, bw, t}, While[c < len && n < nmax, bw = DigitCount[t = n*(n+1)*(n+2)/6, 2, 1] + 1; If[bw <= len && s[[bw]] == 0, c++; s[[bw]] = t]; n++]; s]; seq[30, 10^6] (* Amiram Eldar, Dec 26 2022 *)