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
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
Programs
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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 *)