A385905 Numbers k >= 1 such that digsum(k-r) + ... + digsum(k-1) = digsum(k+1) + ... + digsum(k+r) for some r >= 1 where digsum(i) is the digital sum of i (A007953).

9, 10, 19, 20, 29, 30, 39, 40, 49, 50, 59, 60, 69, 70, 77, 79, 80, 85, 86, 89, 90, 91, 92, 99, 100, 107, 108, 109, 110, 113, 114, 119, 120, 122, 129, 130, 139, 140, 149, 150, 159, 160, 169, 170, 177, 179, 180, 185, 186, 189, 190, 191, 192, 197, 199, 200, 202

Offset: 1

Author

Ctibor O. Zizka, Aug 12 2025

Keywords

• base
• nonn

Comments

Empirical observation: k != A214678(n).

Examples

			For k = 9: the least r = 8, A007953(1) + ... + A007953(8) = A007953(10) + ... + A007953(17), thus k = 9 is a term.
		

Links

• Ctibor O. Zizka, A385905 plot of k vs. r

Crossrefs

Cf. A007953, A214678.

Programs

Mathematica

q[k_] := Module[{s = 0, r = 1}, While[r < k && (r == 1 || s != 0), s += (DigitSum[k-r] - DigitSum[k+r]); r++];1 < r <= k && s ==0]; Select[Range[202], q] (* Amiram Eldar, Aug 12 2025 *)