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A307865 a(n) is the number of natural bases b < 2n+1 such that b^n == -1 (mod 2n+1). 1
0, 1, 2, 3, 0, 5, 6, 1, 8, 9, 0, 11, 0, 1, 14, 15, 0, 1, 18, 1, 20, 21, 0, 23, 0, 1, 26, 1, 0, 29, 30, 1, 0, 33, 0, 35, 36, 1, 0, 39, 0, 41, 4, 1, 44, 9, 0, 1, 48, 1, 50, 51, 0, 53, 54, 1, 56, 1, 0, 1, 0, 1, 2, 63, 0, 65, 0, 1, 68, 69, 0, 1, 0, 1, 74, 75, 0, 1, 78, 1, 0, 81, 0, 83, 0, 1, 86 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n > 0, a(n) = n if and only if 2n+1 is prime.

Note that a(n) < n if and only if 2n+1 is composite.

Conjecture: if 2n+1 is an absolute Euler pseudoprime, then a(n) = 0.

LINKS

Table of n, a(n) for n=0..86.

MATHEMATICA

a[n_] := Length[Select[Range[2n], PowerMod[#, n, 2n+1] == 2n &]]; Array[a, 100] (* Amiram Eldar, May 02 2019 *)

PROG

(PARI) a(n) = sum(b=1, 2*n, Mod(b, 2*n+1)^n == -1); \\ Michel Marcus, May 02 2019

CROSSREFS

Cf. A033181, A053760, A307864.

Sequence in context: A140508 A063956 A128214 * A219695 A267186 A248092

Adjacent sequences:  A307862 A307863 A307864 * A307866 A307867 A307868

KEYWORD

nonn

AUTHOR

Thomas Ordowski, May 02 2019

EXTENSIONS

More terms from Amiram Eldar, May 02 2019

STATUS

approved

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Last modified July 12 06:21 EDT 2020. Contains 335658 sequences. (Running on oeis4.)