A359315 a(n) is the smallest centered triangular number with binary weight n.

1, 10, 19, 46, 31, 235, 631, 1786, 1999, 7669, 7039, 12286, 16381, 180094, 114679, 949231, 2086831, 2883574, 4175839, 12480511, 50329585, 62898151, 132638719, 234618814, 771743710, 2883510271, 4269733885, 8254119871, 17045499901, 33214168831

Offset: 1

Author

Ilya Gutkovskiy, Dec 25 2022

Keywords

• nonn
• base

Examples

			235 is the smallest centered triangular number with binary weight 6 (235_10 = 11101011_2), so a(6) = 235.
		

Links

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

Crossrefs

Cf. A000120, A005448, A089999, A358932, A359316.

Programs

Mathematica

seq[len_,nmax_] := Module[{s = Table[0,{len}], n = 1, c = 0, bw, ct}, While[c < len && n < nmax, bw = DigitCount[ct = 3*n*(n-1)/2 + 1, 2, 1]; If[bw <= len && s[[bw]] == 0, c++; s[[bw]] = ct]; n++]; s]; seq[30, 10^6] (* Amiram Eldar, Dec 26 2022 *)