A358819 Numbers k such that for some r we have w(1) + ... + w(k - 1) = w(k + 1) + ... + w(k + r), where w(i) = A000120(i).

4, 5, 8, 9, 10, 11, 12, 15, 22, 23, 40, 43, 44, 46, 49, 54, 59, 60, 61, 65, 70, 76, 77, 81, 87, 90, 92, 94, 100, 105, 107, 109, 110, 112, 125, 130, 131, 135, 150, 156, 158, 167, 170, 171, 182, 184, 185, 196, 201, 203, 212, 215, 216, 218, 220, 221, 223, 226, 230

Offset

1,1

Comments

1's-counting sequence balancing numbers. Numbers k such that A000788(k-1) + A000788(k) is a term of A000788.

Links

Table of n, a(n) for n=1..59.

Example

k = 4:
w(1) + w(2) + w(3) = w(5) + w(6) = 4.
Thus the balancing number k = 4 is a term. The balancer r = 2.
k = 5:
w(1) + w(2) + w(3) + w(4) = w(6) + w(7) = 5.
Thus the balancing number k = 5 is a term. The balancer r = 2.
w(i) = A000120(i).

Mathematica

With[{m = 500}, w = DigitCount[Range[m], 2, 1]; s = Accumulate[w]; Select[Range[2, m], MemberQ[s, 2*s[[#]] - w[[#]]] &]] (* Amiram Eldar, Dec 02 2022 *)

Crossrefs

Cf. A000120, A000788.

Sequence in context: A292192 A339499 A295150 * A042956 A128217 A288671

Adjacent sequences: A358816 A358817 A358818 * A358820 A358821 A358822

Keyword

nonn

Author

Ctibor O. Zizka, Dec 02 2022

Status

approved