A360372 Numbers k >= 1 such that k divides Sum_{i=1..k} A007088(i).

1, 11, 21, 23, 37, 461, 94101, 14958901, 16364133, 134375017, 192594821, 416095237, 4074380993, 82482257999

Offset: 1

Author

Ctibor O. Zizka, Feb 04 2023

Keywords

• nonn
• more

Comments

The arithmetic mean of the first k binary numbers, taken as decimal numbers, is an integer.

Examples

			k = 11: (1 + 10 + 11 + 100 + 101 + 110 + 111 + 1000 + 1001 + 1010 + 1011) / 11 = 406, thus 11 is a term.
		

Crossrefs

Cf. A007088, A067894.

Programs

Mathematica

s = 0; seq = {}; Do[s += FromDigits[IntegerDigits[k, 2]]; If[Divisible[s, k], AppendTo[seq, k]], {k, 1, 1000}]; seq (* Amiram Eldar, Feb 04 2023 *)

Extensions

a(7)-a(13) from Amiram Eldar, Feb 04 2023

a(14) from Bert Dobbelaere, Feb 14 2023