cp's OEIS Frontend

A380037 For n >= 1, if there exists an m < n such that a(m) = a(n), take the largest such m and set a(n+1) as 1 more than the number of positive terms between a(m+1) and a(n-1). Otherwise, a(n+1) = -1. Start with a(1) = 0.

%I A380037 #33 Jan 23 2025 12:51:36
%S A380037 0,-1,-1,1,-1,2,-1,2,1,3,-1,4,-1,2,4,2,2,1,7,-1,7,1,3,10,-1,5,-1,2,8,
%T A380037 -1,3,5,4,14,-1,5,3,5,2,9,-1,6,-1,2,3,6,3,2,4,13,-1,8,18,-1,3,6,8,4,7,
%U A380037 30,-1,7,2,12,-1,4,6,9,22,-1,5,26
%N A380037 For n >= 1, if there exists an m < n such that a(m) = a(n), take the largest such m and set a(n+1) as 1 more than the number of positive terms between a(m+1) and a(n-1). Otherwise, a(n+1) = -1. Start with a(1) = 0.
%C A380037 This sequence was meant to be a version of A181391 that is more agnostic to individual natural numbers. When a new number is encountered, -1 is used as a placeholder instead of 0, and the -1 terms are not counted when determining the next term in the sequence. So, all natural numbers are in a sense treated equally.
%C A380037 No zeros appear beyond the first term in the sequence. By the definition of the sequence, beyond the first term, all terms must be equal to -1 or an integer of value at least 1.
%C A380037 a(n) < n for all n. a(1) < 1, and for n > 1 either a(n) = -1, which is less than n for all n, or there exists m < n - 1 such that a(m) = a(n - 1) and a(n) <= n - 1 - m which is less than n.
%H A380037 Connor Criss, <a href="/A380037/b380037.txt">Table of n, a(n) for n = 1..10000</a>
%o A380037 (Python)
%o A380037 k = [0]
%o A380037 i = 0
%o A380037 j = 0
%o A380037 n = 0
%o A380037 negatives = 0
%o A380037 total_vals = 0
%o A380037 MAX = 10000
%o A380037 #change value of MAX to modify number of terms generated
%o A380037 index = 0
%o A380037 while(index < MAX):
%o A380037     n = k[-1]
%o A380037     i = len(k) - 2
%o A380037     j = 1
%o A380037     m = 0
%o A380037     while(i > -1):
%o A380037         if(k[i] == k[-1]):
%o A380037             k.append(j)
%o A380037             m = 1
%o A380037             break
%o A380037         if(k[i] != -1 or k[-1] == -1):
%o A380037             j = j + 1
%o A380037         i = i - 1
%o A380037     if m == 0:
%o A380037         k.append(-1)
%o A380037         negatives = negatives + 1
%o A380037     index = index + 1
%o A380037 for x in range(MAX):
%o A380037     print(str(k[x]))
%o A380037 (PARI) a(max_n) = {my(v = [0], r = [], n = 1); while(#v < max_n, r = select(x->x==v[n], v, 1); if(#r>1, v=concat(v, [1+sum(m=r[#r-1]+1, r[#r]-1, v[m]>0)]), v=concat(v,[-1])); n++); v} \\ _Thomas Scheuerle_, Jan 11 2025
%Y A380037 Similar to the Van Eck sequence A181391.
%K A380037 sign
%O A380037 1,6
%A A380037 _Connor Criss_, Jan 10 2025