A276664 -id:A276664 - cp's OEIS frontend

A276695 P-defects p - N(p) of the congruence y^2 == x^3 - x^2 + 4*x - 4 (mod p) for primes p, where N(p) is the number of solutions given for p = prime(n) by A276664(n).

0, 2, -1, -2, 0, 2, -6, 4, -6, 6, 4, 2, 6, 10, 6, -6, -12, 2, -2, 12, 2, -8, -6, -6, 2, 6, -14, 6, 2, -6, -2, 0, 18, 4, -6, -20, -22, 10, -18, -6, 12, -10, 12, 26, 18, -8, 16, 10, 6, 14, -6, 24, 14, 0, -6, 18, 18, -20, 26, 6

Offset: 1

Seiichi Manyama, Sep 14 2016

sign

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A273163, A276664.

a(n) = prime(n) - A276664(n), n >= 1, where A276664(n) is the number of solutions to the congruence y^2 == x^3 - x^2 + 4*x - 4 (mod prime(n)).

If prime(n) == 1 (mod 4), a(n) = A273163(n). If prime(n) == 3 (mod 4), a(n) = -A273163(n).

A276030 Primes p such that A272207(p) = p.

Original entry on oeis.org

2, 11, 131, 251, 491, 599, 1439, 3371, 5639, 5879, 6971, 7079, 8039, 8291, 9839, 10799, 11171, 12119, 14879, 16931, 17159, 18839, 23039, 23159, 25919, 50291, 53411, 53639, 59051, 69371, 74771, 74891, 75239, 81119, 81359, 117839, 119039, 126839, 130811, 131771

Offset: 1

Seiichi Manyama, Sep 10 2016

nonn

These terms are the primes prime(A273163(n)) for which A273163(n) = 0.
These terms are the primes for which A276491(p) == 0 (mod p).
These terms are the primes p = prime(n) for which A276664(n) = p.
These terms are the primes prime(A276695(n)) for which A276695(n) = 0.

			2 = A272207(1) = prime(1),
11 = A272207(5) = prime(5),
131 = A272207(32) = prime(32),
251 = A272207(54) = prime(54).

Cf. A272207, A273163, A276491, A276664, A276695.

cp's OEIS Frontend

A276695 P-defects p - N(p) of the congruence y^2 == x^3 - x^2 + 4*x - 4 (mod p) for primes p, where N(p) is the number of solutions given for p = prime(n) by A276664(n).

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A276030 Primes p such that A272207(p) = p.

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