A358931 a(n) is the smallest n-gonal pyramidal number with binary weight n.

35, 30, 405, 95, 6860, 765, 28855, 7923, 96760, 380091, 259064, 915915, 3845501, 1436415, 32471830, 11992255, 62904941, 182171613, 266182382, 670936891, 939382515, 2533347310, 30530860911, 1876688877, 16972115903, 201845686175, 529756691451, 409027868651, 2713039388125

Offset: 3

Author

Ilya Gutkovskiy, Dec 06 2022

Keywords

• nonn
• base

Examples

			405 is the smallest pentagonal pyramidal number with binary weight 5 (405_10 = 110010101_2), so a(5) = 405.
		

Links

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

Crossrefs

Cf. A000120, A358930, A358932.

Programs

Mathematica

p[n_, k_] := k*(k + 1)*((n - 2)*k + 5 - n)/6; a[n_] := Module[{k = 1, pk}, While[DigitCount[pk = p[n, k], 2, 1] != n, k++]; pk]; Array[a, 30, 3] (* Amiram Eldar, Dec 09 2022 *)