A386971 Numbers k >= 1 such that w(k-r) + ... + w(k-1) = w(k+1) + ... + w(k+r) for some r >= 1 where w(i) is the binary weight of i (A000120).

3, 4, 7, 8, 11, 12, 14, 15, 16, 17, 19, 20, 23, 24, 27, 28, 29, 31, 32, 34, 35, 36, 39, 40, 43, 44, 46, 47, 48, 49, 51, 52, 55, 56, 58, 59, 60, 63, 64, 67, 68, 69, 71, 72, 75, 76, 78, 79, 80, 81, 83, 84, 87, 88, 91, 92, 93, 95, 96, 98, 99, 100, 103, 104, 107

Offset: 1

Author

Ctibor O. Zizka, Aug 11 2025

Keywords

• nonn
• base

Comments

r = 1 for k from A047457, k = 8*x - 5 or k = 8*x - 4, x >= 1.

r = 2 for k = 32*x - 18, (2* 7th row of A097586) or k = 32*x - 15, (10th row of A097586), x >= 1.

Examples

			For k = 7: A000120(4) + A000120(5) + A000120(6) = A000120(8) + A000120(9) + A000120(10), thus 7 is a term.
		

Links

• Ctibor O. Zizka, A386971 plot of k vs. r

Crossrefs

Cf. A000120, A047457, A097586.

Programs

Mathematica

q[k_] := Module[{s = 0, r = 1}, While[r < k && (r == 1 || s != 0), s += (DigitSum[k-r, 2] - DigitSum[k+r, 2]); r++]; 1 < r <= k && s ==0]; Select[Range[120], q] (* Amiram Eldar, Aug 12 2025 *)