A215653 a(n) = smallest positive m such that m^2=1+k*n with positive k.

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, 28, 11, 30, 15, 10, 33, 6, 17, 36, 37, 14, 9, 40, 13, 42, 21, 19, 45, 46, 7, 48, 49, 16, 25, 52, 53, 21, 13, 20, 57, 58, 11, 60, 61, 8, 31, 14, 23, 66, 33, 22, 29

Offset

1,1

Comments

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

References

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

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A070667, A076942.

Sequence in context: A336860 A216209 A289172 * A358503 A327666 A286717

Adjacent sequences: A215650 A215651 A215652 * A215654 A215655 A215656

Keyword

nonn

Author

Zak Seidov, Aug 19 2012

Status

approved