A332777 - OEIS

A332777

a(n) = k^2 mod p where p is the n-th prime and of the form 6k-1 or 6k+1.

1, 1, 4, 4, 9, 9, 16, 25, 25, 36, 8, 6, 17, 28, 41, 39, 54, 2, 71, 11, 30, 47, 62, 87, 83, 3, 106, 22, 60, 91, 118, 112, 29, 21, 48, 77, 116, 149, 5, 176, 69, 59, 104, 94, 170, 31, 82, 70, 123, 166, 154, 7, 50, 95, 142, 128, 177, 242, 228, 57, 145, 216, 200, 273

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OFFSET

3,3

COMMENTS

Offset is 3 because 5=prime(3) is the first prime of the given form. It is provable that if 6m-1 and 6m+1 are a pair of twin primes, then for all k, 0<k<m, and p being a prime of the form 6k-1 or 6k+1 then m^2 is not equivalent to k^2 mod p.

LINKS

Table of n, a(n) for n=3..66.

PROG

(PARI) a(n) = {my(p=prime(n), k); if (((p-1) % 6) == 0, k = (p-1)/6, k = (p+1)/6); k^2 % p; } \\ Michel Marcus, Jun 09 2020

CROSSREFS

Cf. A002476, A007528, A024699.

Sequence in context: A145445 A008794 A075709 * A238629 A192032 A116682

Adjacent sequences: A332774 A332775 A332776 * A332778 A332779 A332780

KEYWORD

nonn

AUTHOR

Keith Backman, Jun 08 2020

EXTENSIONS

More terms from Michel Marcus, Jun 09 2020

STATUS

approved