A385655 Numbers k >= 0 such that k = digsum(k) + digsum(k+1) + ... + digsum(k+r) for some r >= 0 where digsum(i) is the digital sum of i (A007953).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 17, 19, 20, 22, 28, 29, 34, 37, 38, 46, 47, 51, 56, 65, 70, 79, 88, 91, 94, 95, 103, 105, 106, 112, 114, 118, 121, 123, 130, 132, 137, 141, 150, 157, 166, 175, 178, 184, 192, 200, 203, 205, 220, 222, 235, 241, 246, 260

Offset: 1

Author

Ctibor O. Zizka, Aug 03 2025

Keywords

• base
• nonn

Examples

			For k = 10: 10 = A007953(10) + A007953(11) + A007953(12) + A007953(13) = 10, thus 10 is a term.
		

Links

• Ctibor O. Zizka, Relationship between k and r

Crossrefs

Cf. A007953.

Programs

Mathematica

q[k_] := Module[{s = 0, m = k}, While[s < k, s += DigitSum[m]; m++]; s == k]; Select[Range[0, 300], q] (* Amiram Eldar, Aug 03 2025 *)

PARI

isok(k) = my(s=sumdigits(k), t=k+1); while (s < k, s+=sumdigits(t); t++); s==k; \\ Michel Marcus, Aug 04 2025

Python

from itertools import count, islice
def A385655_gen(startvalue=0): # generator of terms >= startvalue
    for k in count(max(startvalue,0)):
        s, r = 0, k
        while sA385655_list = list(islice(A385655_gen(),40)) # Chai Wah Wu, Aug 09 2025