A065907 First solution mod p of x^4 = 2 for primes p such that only two solutions exist.

2, 8, 15, 17, 15, 3, 48, 4, 16, 34, 33, 47, 98, 92, 68, 63, 114, 78, 153, 157, 107, 36, 156, 115, 86, 58, 222, 297, 57, 6, 18, 235, 66, 142, 221, 395, 227, 33, 120, 408, 368, 131, 301, 408, 253, 149, 318, 405, 459, 121, 30, 206, 122, 28, 543, 472, 88, 283, 696, 246

Offset

1,1

Comments

Conjecture: no integer occurs more than three times in this sequence. Confirmed for the first 2399 terms of A007522 (primes < 100000). There are integers which do occur thrice, e.g. 221, 1159.

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = first (least) solution mod p of x^4 = 2, where p is the n-th prime such that x^4 = 2 has only two solutions mod p, i.e. p is the n-th term of A007522.

Example

a(8) = 4, since 127 is the eighth term of A007522 and 4 is the first solution mod 127 of x^4 = 2.

Prog

(PARI): a065907(m) = local(s); forprime(p = 2, m, s = []; for(x = 0, p-1, if(x^4%p == 2%p, s = concat(s, [x]))); if(matsize(s)[2] == 2, print1(s[1], ", "))) a065907(1600)

Crossrefs

Cf. A040098, A007522, A065908.

Sequence in context: A059449 A272930 A140973 * A031272 A277139 A213082

Adjacent sequences: A065904 A065905 A065906 * A065908 A065909 A065910

Keyword

nonn

Author

Klaus Brockhaus, Nov 29 2001

Status

approved