A082484 First of four consecutive primes p, q, r, s such that neither of the congruences p^x+q^x = r (mod s) and q^x-p^x = r (mod s) has a solution.

3, 53, 71, 97, 109, 127, 137, 149, 151, 179, 197, 239, 293, 311, 401, 419, 431, 439, 457, 467, 503, 557, 563, 601, 619, 641, 643, 653, 673, 769, 887, 907, 971, 991, 1021, 1031, 1093, 1103, 1123, 1151, 1297, 1361, 1367, 1373, 1427, 1447, 1459, 1471, 1481

Offset

1,1

Comments

Is this sequence infinite?

Links

Table of n, a(n) for n=1..49.

Formula

a(n) = prime(A082475(n)).

Example

2 is not in the sequence because 2^1+3^1 = 5 (mod 7).
17 is not in the sequence because 19^4-17^4 = 23 (mod 29).

Prog

(PARI) { for (p = 1, 300, f = 0; for (x = 1, prime(p + 3) - 1, if ((prime(p + 1)^x + prime(p)^x - prime(p + 2))%prime(p + 3) == 0 || (prime(p + 1)^x - prime(p)^x - prime(p + 2))%prime(p + 3) == 0, f = 1; break)); if (f == 0, print(prime(p)))) }

Crossrefs

Cf. A082371, A082475.

Sequence in context: A228452 A269458 A288867 * A187805 A178608 A106997

Adjacent sequences: A082481 A082482 A082483 * A082485 A082486 A082487

Keyword

easy,nonn,less

Author

Cino Hilliard, May 11 2003

Extensions

Edited and extended by David Wasserman, Oct 12 2006

Status

approved