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
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.
Programs
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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
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