A065908 Second solution mod p of x^4 = 2 for primes p such that only two solutions exist.

5, 15, 16, 30, 56, 76, 55, 123, 135, 133, 158, 152, 125, 147, 195, 208, 197, 281, 214, 226, 324, 403, 307, 364, 401, 445, 377, 310, 574, 641, 701, 492, 677, 609, 602, 444, 636, 854, 791, 511, 599, 852, 690, 623, 786, 914, 769, 698, 692, 1102, 1201, 1073

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). In this section, there are no integers which do occur thrice.

Links

Table of n, a(n) for n=1..52.

Formula

a(n) = second (largest) 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(3) = 16, since 31 is the third term of A007522 and 16 is the second solution mod 31 of x^4 = 2.

Prog

(PARI): a065908(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[2], ", "))) a065908(1400)

Crossrefs

A040098, A007522, A065907.

Sequence in context: A030486 A101238 A109161 * A297124 A166503 A231720

Adjacent sequences: A065905 A065906 A065907 * A065909 A065910 A065911

Keyword

nonn

Author

Klaus Brockhaus, Nov 29 2001

Status

approved