A359318 a(n) is the smallest square pyramidal number with binary weight n.

0, 1, 5, 14, 30, 55, 819, 506, 1785, 1015, 16206, 51039, 98021, 81375, 1113775, 964535, 2607099, 5494655, 1048061, 6029275, 50331190, 356343295, 534555645, 516941815, 4021378559, 2143222510, 12842950505, 34091142526, 68651299705, 124545644405, 273736383990

Offset: 0

Author

Ilya Gutkovskiy, Dec 25 2022

Keywords

• nonn
• base

Examples

			819 is the smallest square pyramidal number with binary weight 6 (819_10 = 1100110011_2), so a(6) = 819.
		

Links

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

Crossrefs

Cf. A000120, A000330, A089998, A358931, A359317.

Programs

Maple

V:= Array(0..40): count:= 0:
for k from 1 while count < 40 do
  m:= k*(k+1)*(2*k+1)/6;
  w:= convert(convert(m,base,2),`+`);
  if w <= 40 and V[w] = 0 then
    count:= count+1; V[w]:= m;
  fi
od:
convert(V,list); # Robert Israel, Dec 26 2022

Mathematica

seq[len_,nmax_] := Module[{s = Table[0,{len}], n = 0, c = 0, bw, sp}, While[c < len && n < nmax, bw = DigitCount[sp = n*(n+1)*(2*n+1)/6, 2, 1] + 1; If[bw <= len && s[[bw]] == 0, c++; s[[bw]] = sp]; n++]; s]; seq[31, 10^6] (* Amiram Eldar, Dec 26 2022 *)