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
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
Programs
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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 *)