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

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, Table of n, a(n) for n = 0..9999

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 *)

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 A068627

Adjacent sequences: A374962 A374963 A374965 * A374968 A374969 A374970

Keyword

nonn,easy,nice,new

Author

Bryle Morga, Jul 25 2024

Status

approved