cp's OEIS Frontend

A343039 a(1) = 1, for n > 1, a(n) is the smallest positive integer for which a(n-1) + n + a(n) is a square.

%I A343039 #18 Apr 04 2021 01:09:35
%S A343039 1,1,5,7,4,6,3,5,2,4,1,3,9,2,8,1,7,11,6,10,5,9,4,8,3,7,2,6,1,5,13,4,
%T A343039 12,3,11,2,10,1,9,15,8,14,7,13,6,12,5,11,4,10,3,9,2,8,1,7,17,6,16,5,
%U A343039 15,4,14,3,13,2,12,1,11
%N A343039 a(1) = 1, for n > 1, a(n) is the smallest positive integer for which a(n-1) + n + a(n) is a square.
%H A343039 Todor Szimeonov, <a href="https://newprimax.blogspot.com/2021/04/a-completive-sequence.html">A completive sequence</a>.
%t A343039 d[n_] := Floor[Sqrt[n] + 1]^2 - n; a[1] = 1; a[n_] := a[n] = d[a[n - 1] + n]; Array[a, 100] (* _Amiram Eldar_, Apr 03 2021 *)
%o A343039 (Python)
%o A343039 from math import isqrt
%o A343039 def aupton(terms):
%o A343039   alst = [1]
%o A343039   for n in range(2, terms+1):
%o A343039     alst.append((isqrt(alst[-1] + n)+1)**2 - alst[-1] - n)
%o A343039   return alst
%o A343039 print(aupton(79)) # _Michael S. Branicky_, Apr 03 2021
%K A343039 nonn
%O A343039 1,3
%A A343039 _Todor Szimeonov_, Apr 03 2021