A359316 a(n) is the smallest centered square number with binary weight n.

1, 5, 13, 85, 61, 221, 761, 1013, 2813, 12013, 23545, 54781, 16381, 196565, 425965, 770041, 3137513, 7663613, 13629421, 20962813, 63946741, 121602013, 192805885, 499122013, 989724541, 2411720701, 6435110905, 17162301181, 29929502461, 63753420281

Offset: 1

Author

Ilya Gutkovskiy, Dec 25 2022

Keywords

• nonn
• base

Examples

			221 is the smallest centered square number with binary weight 6 (221_10 = 11011101_2), so a(6) = 221.
		

Links

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

Crossrefs

Cf. A000120, A001844, A089998, A358932, A359315.

Programs

Mathematica

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