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A374966
a(n) = 0 if n has appeared in the sequence before, otherwise a(n) = a(n-1) + n. Start with a(0) = 0.
3
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, Log log scatterplot of a(n), n = 0..2^20, showing zeros instead as 1/2 in red, otherwise blue.
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
KEYWORD
nonn,easy,nice
AUTHOR
Bryle Morga, Jul 25 2024
STATUS
approved