

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
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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), 173178.


LINKS



FORMULA



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



KEYWORD

nonn


AUTHOR



STATUS

approved



