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

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

Offset: 1

Author

Bryle Morga, Jul 29 2024

Keywords

• nonn
• more

Crossrefs

Cf. A374966, A375060.

Programs

Mathematica

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 *)

Python

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

Formula

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

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