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

Author

Bryle Morga, Jul 25 2024

Keywords

• nonn
• easy
• nice

Comments

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

The set of numbers appearing in this sequence is the union of {A375060(n)} and {A375060(n) + 1}. - Yifan Xie, Apr 09 2025

Examples

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

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.

Crossrefs

Cf. A375060, A375065.

Programs

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 *)

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