A375060 Values of k for which A374966(k) = 0.

0, 3, 9, 15, 21, 22, 30, 33, 46, 47, 51, 60, 63, 69, 70, 72, 90, 97, 98, 105, 123, 125, 129, 142, 147, 153, 159, 180, 182, 183, 195, 199, 213, 214, 219, 222, 253, 259, 261, 262, 270, 276, 287, 297, 298, 300, 309, 321, 327, 330, 342, 369, 370, 375, 381, 385, 393, 401, 402, 429, 430, 431, 432, 441

Offset: 1

Author

Bryle Morga, Jul 29 2024

Keywords

• nonn
• easy

Comments

It seems that this sequence grows linearly but this is unproven.

Examples

			21 is a term; A374966(11) = 21 and by the definition of A374966, A374966(21) = 0.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A374966.

Programs

Mathematica

nn = 2^20; c[] := False; j = 0; c[0] = True; {j}~Join~Reap[Do[If[c[n], k = 0; Sow[n], k = j + n]; Set[{c[k], j}, {True, k}], {n, nn}] ][[-1, 1]] (* _Michael De Vlieger, Jul 29 2024 *)

Python

from itertools import count, islice
def agen(): # generator of terms
    seen, an = {0}, 0
    for n in count(1):
        if an == 0: yield n-1
        an = 0 if n in seen else an + n
        seen.add(an)
print(list(islice(agen(), 64))) # Michael S. Branicky, Jul 29 2024

Formula

A374966(a(n)) = 0.

a(n) ~ c*n, empirically, with c = 7.42...