This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
A005132(111)=40, A005132(112)=152, A005132(113)=265, A005132(114)=379, A005132(115)=494 - four increasing terms starting from #111, so a(4) = 111.
After we have found A005132(6)=13, we attempt to subtract 7 from 13 to get a(7). However, this would give 6, which is a collision, since we already have A005132(3)=6. Furthermore, 6 is larger than any collision we have so far avoided. So 7 (the index of the term of A005132 that we were constructing), gets added to the current sequence (it is a(3)).
import math
n_max = 1000000
a_last = 0
list1 = [a_last]
print(0)
for n in range(1, n_max+1):
m = a_last - n
if m >= 0 and m not in list1:
a = m
else:
a = a_last + math.ceil(n/2)
list1.append(a)
print(a)
a_last = a
r[-1] = r[0] = 0; r[n_] := r[n] = If[(d = r[n - 1] - n) >= 0 && FreeQ[Array[r, n, 0], d], d, r[n - 1] + n]; a[n_] := (r[2*n - 1] + r[2*n])/4; Array[a, 100] (* Amiram Eldar, Sep 02 2022 *)
recaman(N)={ my(s, t, v=vector(N)); for(n=1, N, s=bitor(s, 1<A005132
lista(nn) = my(v=recaman(2*nn+2)); vector(nn, k, v[2*k-1] + v[2*k])/4; \\ Michel Marcus, Sep 13 2022
from itertools import count, islice def A356870_gen(): # generator of terms b, aset = 0, set() for n in count(1): aset.add(b) a, b = b, c if (c:=b-n)>=0 and c not in aset else b+n if not n&1: yield a+b>>2 A356870_list = list(islice(A356870_gen(),30)) # Chai Wah Wu, Sep 15 2022
a(0) = (0-0)/2, a(1) = (1-1)/2, a(2) = (3-3)/2, a(3) = (6-6)/2, a(4) = (10-2)/2, a(5) = (15-7)/2 ... .
E.g., going from r(4)=2 to r(5)=7 to r(6)=13 we increase twice in a row, so 6 is a member. Going from r(21)=63 to r(22)=41 to r(23)=18 we decrease twice in a row, so 23 is a member.
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