A374966 -id:A374966 - cp's OEIS frontend

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

Bryle Morga, Jul 29 2024

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

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

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

Cf. A374966.

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 *)

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

A374966(a(n)) = 0.

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

A375065 Starting index of the first length-n (exactly) run of zeros in A374966.

Original entry on oeis.org

0, 21, 1798, 429, 10727, 431795, 8394951, 171051143

Offset: 1

Bryle Morga, Jul 29 2024

Cf. A374966, A375060.

nn = 2^24; c[] := False; j = m = 0; r = 1; c[0] = True; s = Monitor[Reap[Do[If[c[n], k = 0; r++, k = j + n; If[j == 0, Sow[{r, n - r}]; If[r > m, m = r]; r = 0]]; Set[{c[k], j}, {True, k}], {n, nn}]][[-1, 1]], n]; TakeWhile[Array[s[[FirstPosition[s[[;; , 1]], #][[1]], -1]] &, m], IntegerQ] (* _Michael De Vlieger, Jul 29 2024 *)

from itertools import count, islice
def agen(): # generator of terms
    seen, an, zcount, zdict, zn = {0}, 0, 0, dict(), 1
    for n in count(1):
        if an == 0:
            zcount += 1
        else:
            if zcount not in zdict:
                zdict[zcount] = n-zcount-1
            while zn in zdict: yield zdict[zn]; zn += 1
            zcount = 0
        an = 0 if n in seen else an + n
        seen.add(an)
print(list(islice(agen(), 7))) # Michael S. Branicky, Jul 29 2024

a(2) = 21; A374966(21) = A374966(22) = 0.

a(3) = 1798; A374966(1798) = A374966(1799) = A374966(1800) = 0.

cp's OEIS Frontend

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

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