A374966 a(n) = 0 if n has appeared in the sequence before, otherwise a(n) = a(n-1) + n. Start with a(0) = 0.

0, 1, 3, 0, 4, 9, 15, 22, 30, 0, 10, 21, 33, 46, 60, 0, 16, 33, 51, 70, 90, 0, 0, 23, 47, 72, 98, 125, 153, 182, 0, 31, 63, 0, 34, 69, 105, 142, 180, 219, 259, 300, 342, 385, 429, 474, 0, 0, 48, 97, 147, 0, 52, 105, 159, 214, 270, 327, 385, 444, 0, 61, 123, 0, 64, 129, 195, 262, 330, 0, 0

Offset

0,3

Comments

The sequence seems to grow linearly. The average distance between zeros in the sequence appears to converge to about 7.42.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..16384 (terms 0..9999 from Bryle Morga).

Michael De Vlieger, Log log scatterplot of a(n), n = 0..2^20, showing zeros instead as 1/2 in red, otherwise blue.

Bryle Morga, Plot of the average distance between zeros for first 250000 terms.

Example

a(1) = a(0) + 1 = 1.
a(2) = a(1) + 2 = 3.
a(3) = 0 because a(2) = 3.

Mathematica

a={0}; For[n=1, n<=70, n++, If[MemberQ[a, n], AppendTo[a, 0], AppendTo[a, Last[a]+n]]]; a (* Stefano Spezia, Jul 26 2024 *)
Fold[If[MemberQ[#1, #2], Append[#1, 0], Append[#1, Last[#1] + #2]] &, {0}, Range @ 10^5] (* Mikk Heidemaa, Oct 05 2024 *)

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    seen, an = {0}, 0
    for n in count(1):
        yield an
        an = 0 if n in seen else an + n
        seen.add(an)
print(list(islice(agen(), 71))) # Michael S. Branicky, Jul 25 2024

Crossrefs

Sequence in context: A330420 A072329 A068630 * A309764 A079406 A378505

Adjacent sequences: A374963 A374964 A374965 * A374967 A374968 A374969

Keyword

nonn,easy,nice

Author

Bryle Morga, Jul 25 2024

Status

approved