cp's OEIS Frontend

A318135 The 10-adic integer a = ...1588948901 satisfying a^2 + 1 = b, b^2 + 1 = c, c^2 + 1 = d, d^2 + 1 = e, e^2 + 1 = f, and f^2 + 1 = a.

%I A318135 #27 Nov 19 2022 21:01:21
%S A318135 1,0,9,8,4,9,8,8,5,1,0,2,0,1,1,9,3,5,1,0,7,9,3,2,1,8,0,0,1,2,2,4,8,5,
%T A318135 9,2,2,4,6,7,7,1,3,3,2,7,7,4,8,2,8,5,6,0,8,5,7,1,6,6,7,4,8,0,0,5,1,4,
%U A318135 9,8,8,1,1,4,6,4,7,4,4,4,9,5,8,8,7,0,3,1,3,3,2,5,8,4,6,7,2,4,0,9,8,0,0,0,4,1,7,5,8,7,0,1,4,5,9,4,0,9,4,5,3,3,5,8,0,8,2,5,9,5,9,8,2,3,1,0,4,7,7,6,6,4,4,0,7,3,1,1,7,6
%N A318135 The 10-adic integer a = ...1588948901 satisfying a^2 + 1 = b, b^2 + 1 = c, c^2 + 1 = d, d^2 + 1 = e, e^2 + 1 = f, and f^2 + 1 = a.
%C A318135 Data generated using MATLAB.
%C A318135 Conjecture: Let r(k) = the smallest positive residue of A003095(6*k+1) mod 10^(6*k+1). Then the first 2*k + 2 digits of r(k), reading from right to left, give the first 2*k + 2 digits of this 10-adic number. For example with k = 5, r(k) = 2121286728960294(201588948901) gives the first 12 digits correctly. - _Peter Bala_, Nov 14 2022
%H A318135 Seiichi Manyama, <a href="/A318135/b318135.txt">Table of n, a(n) for n = 0..1000</a>
%e A318135 901^2 + 1 == 802 (mod 10^3), 802^2 + 1 == 205 (mod 10^3), 205^2 + 1 == 26 (mod 10^3), 26^2 + 1 == 677 (mod 10^3), 677^2 + 1 == 330 (mod 10^3), and 330^2 + 1 == 901 (mod 10^3), so 1 0 9 comprise the sequence's first three terms.
%Y A318135 Cf. A018247, A003095, A318136 (b), A318137 (c), A318138 (d), A318139 (e), A318140 (f).
%K A318135 nonn,base
%O A318135 0,3
%A A318135 _Patrick A. Thomas_, Aug 19 2018