A215653 - OEIS

%I #13 Feb 16 2019 11:56:09

%S 2,3,2,3,4,5,6,3,8,9,10,5,12,13,4,7,16,17,18,9,8,21,22,5,24,25,26,13,

%T 28,11,30,15,10,33,6,17,36,37,14,9,40,13,42,21,19,45,46,7,48,49,16,25,

%U 52,53,21,13,20,57,58,11,60,61,8,31,14,23,66,33,22,29

%N a(n) = smallest positive m such that m^2=1+k*n with positive k.

%C Apparently a(n>2)=A070667(n). Note the linear patterns in the graph.

%D Dorin Andrica, Vlad Crişan, The smallest nontrivial solution to x^k == 1 (mod n) ..., Amer. Math. Monthly 126 (2019), 173-178.

%H Zak Seidov, <a href="/A215653/b215653.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = sqrt(1+n*A076942(n)).

%e a(1)=2, k=3; a(2)=3, k=4; a(3)=2, k=1; a(1000)=249, k=62.

%t Flatten[{2,Table[Select[Range[2,1000],PowerMod[#,2,k]==1&,1],{k,2,1000}]}] (*first 1000 terms*)

%Y Cf. A070667, A076942.

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 19 2012