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A035091 Smallest prime == 1 mod (n^2). 1
2, 5, 19, 17, 101, 37, 197, 193, 163, 101, 727, 433, 677, 197, 1801, 257, 3469, 1297, 10831, 401, 883, 1453, 12697, 577, 11251, 677, 1459, 3137, 10093, 1801, 15377, 12289, 2179, 3469, 7351, 1297, 5477, 18773, 9127, 1601, 16811, 3529, 22189, 11617 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Smallest prime of form (n^2)*k+1, i.e., an arithmetic progression with n^2 differences; k is the subscript of the progressions.

LINKS

Table of n, a(n) for n=1..44.

Index entries for sequences related to primes in arithmetic progressions

EXAMPLE

a(5)=101 because in 5^2k + 1 = 25k + 1 progression k=4 generates the smallest prime (this is 101) and 26, 51, and 76 are composite.

MATHEMATICA

Join[{2}, With[{prs=Prime[Range[2500]]}, Flatten[Table[Select[prs, Mod[#, n^2] == 1&, 1], {n, 50}]]]] (* Harvey P. Dale, Feb 24 2013 *)

CROSSREFS

Analogous case is A034694. Special case is A002496.

Cf. A070844 to A070858, A061092, A035095.

Sequence in context: A323706 A125765 A068873 * A045367 A045368 A215426

Adjacent sequences:  A035088 A035089 A035090 * A035092 A035093 A035094

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified December 5 21:00 EST 2019. Contains 329779 sequences. (Running on oeis4.)