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

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). There are integers which do occur thrice, e.g. 221, 1159.

Examples

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

Crossrefs

Cf. A040098, A007522, A065908.

Programs

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)

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.