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 A215653 a(n) = smallest positive m such that m^2=1+k*n with positive k. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 1 09:59 EST 2024. Contains 370432 sequences. (Running on oeis4.)