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

1,2

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Centered Square Number

Index entries for sequences related to binary expansion of n

Example

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

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 *)

Crossrefs

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

Sequence in context: A214536 A363015 A324418 * A165262 A092955 A190949

Adjacent sequences: A359313 A359314 A359315 * A359317 A359318 A359319

Keyword

nonn,base

Author

Ilya Gutkovskiy, Dec 25 2022

Status

approved