cp's OEIS Frontend

A347595 a(0) = 1; for n>0, a(n) is the smallest positive integer that has not previously occurred such that a(n-1)^2 + n^2 + a(n) is a square.

%I A347595 #8 Sep 18 2021 01:00:54
%S A347595 1,2,8,27,39,54,73,98,133,186,273,426,709,1250,2305,4386,8517,16746,
%T A347595 33169,65978,131557,262674,524865,1049202,2097829,4195034,8389393,
%U A347595 16778058,33555333,67109826,134218753,268436546,536872069,1073743050,2147484945,4294968666,8589936037,17179870706
%N A347595 a(0) = 1; for n>0, a(n) is the smallest positive integer that has not previously occurred such that a(n-1)^2 + n^2 + a(n) is a square.
%C A347595 This sequence uses the same rules as A347594 except here all numbers must be unique. Up to 10^5 terms all terms are larger than the previous term; it is unknown if this holds for all terms as n->infinity.
%e A347595 a(1) = 2 as a(0)^2 + 1^2 = 1 + 1 = 2, and 2 + 2 = 4 = 2^2 is the next smallest square.
%e A347595 a(2) = 8 as a(1)^2 + 2^2 = 4 + 4 = 8, and 8 + 8 = 16 = 4^2. Note that although 8 + 1 = 9 = 3^2, 1 cannot be chosen as a(0) = 1.
%e A347595 a(3) = 27 as a(2)^2 + 3^2 = 64 + 9 = 73 and 73 + 27 = 100 = 10^2.  Note that although 73 + 8 = 81 = 9^2, 8 cannot be chosen as a(2) = 8.
%e A347595 a(4) = 39 as a(3)^2 + 4^2 = 729 + 16 = 745, and 745 + 39 = 784 = 28^2 is the next smallest square.
%Y A347595 Cf. A347594, A000290, A103605, A009000, A005408, A347754.
%K A347595 nonn
%O A347595 0,2
%A A347595 _Scott R. Shannon_, Sep 08 2021