A374966 - OEIS

%I #41 Nov 20 2024 10:02:52

%S 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,

%T 98,125,153,182,0,31,63,0,34,69,105,142,180,219,259,300,342,385,429,

%U 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

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

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

%H Michael De Vlieger, <a href="/A374966/b374966.txt">Table of n, a(n) for n = 0..16384</a> (terms 0..9999 from Bryle Morga).

%H Michael De Vlieger, <a href="/A374966/a374966_1.png">Log log scatterplot of a(n)</a>, n = 0..2^20, showing zeros instead as 1/2 in red, otherwise blue.

%H Bryle Morga, <a href="/A374966/a374966.png">Plot of the average distance between zeros for first 250000 terms.</a>

%e a(1) = a(0) + 1 = 1.

%e a(2) = a(1) + 2 = 3.

%e a(3) = 0 because a(2) = 3.

%t 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 *)

%t Fold[If[MemberQ[#1, #2], Append[#1, 0], Append[#1, Last[#1] + #2]] &, {0}, Range @ 10^5] (* _Mikk Heidemaa_, Oct 05 2024 *)

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     seen, an = {0}, 0

%o     for n in count(1):

%o         yield an

%o         an = 0 if n in seen else an + n

%o         seen.add(an)

%o print(list(islice(agen(), 71))) # _Michael S. Branicky_, Jul 25 2024

%K nonn,easy,nice

%O 0,3

%A _Bryle Morga_, Jul 25 2024