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

Author

Klaus Brockhaus, Nov 29 2001

Keywords

• nonn

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.

Examples

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

Crossrefs

A040098, A007522, A065907.

Programs

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)

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.