A065909 First solution mod p of x^4 = 2 for primes p such that more than two solutions exist.

18, 5, 27, 28, 35, 46, 131, 48, 252, 104, 45, 123, 51, 9, 69, 77, 51, 177, 472, 261, 55, 117, 224, 562, 12, 264, 273, 132, 127, 500, 17, 197, 107, 36, 206, 671, 127, 159, 137, 684, 329, 564, 316, 314, 197, 98, 661, 925, 461, 170, 930, 151, 1081, 333, 434, 924

Offset: 1

Author

Klaus Brockhaus, Nov 29 2001

Keywords

• nonn

Comments

Conjecture: no integer occurs more than three time in this sequence. Confirmed for the first 1182 terms of A014754 (primes < 100000). There are integers which do occur thrice, e.g. 6624. Moreover, no integer is first, second, third or fourth solution for more than three primes. Confirmed for the first 2399 terms of A007522 and the first 1182 terms of A014754 (primes < 100000).

Examples

			a(3) = 27, since 113 is the third term of A014754, 27, 47, 66 and 86 are the solutions mod 113 of x^4 = 2 and 27 is the least one.
		

Crossrefs

Cf. A040098, A007522, A014754, A065910, A065911, A065912.

Programs

PARI

a065909(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],",")))
a065909(4000)

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 more than two solutions mod p, i.e. p is the n-th term of A014754.

Extensions

Definition corrected by Harvey P. Dale, Apr 16 2015