A065911 Third solution mod p of x^4 = 2 for primes p such that more than two solution exists.

48, 81, 66, 162, 211, 190, 179, 251, 299, 299, 385, 416, 526, 827, 736, 766, 936, 586, 703, 779, 639, 999, 980, 808, 1137, 975, 1314, 1458, 1557, 1112, 1041, 1563, 1415, 1150, 1681, 1355, 1723, 1623, 1468, 1303, 1398, 1702, 2265, 1958, 1787, 2668, 2000

Offset

1,1

Comments

Conjecture: no integer occurs more than three time in this sequence. Confirmed for the first 1182 terms of A014754 (primes < 100000). In this section, there are no integers which do occur thrice. 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).

Links

Table of n, a(n) for n=1..47.

Formula

a(n) = third 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.

Example

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

Prog

(PARI): a065911(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[3], ", "))) a065911(3000)

Crossrefs

Cf. A040098, A007522, A014754, A065909, A065910, A065912.

Sequence in context: A030628 A178739 A261548 * A260841 A260767 A211722

Adjacent sequences: A065908 A065909 A065910 * A065912 A065913 A065914

Keyword

nonn

Author

Klaus Brockhaus, Nov 29 2001

Status

approved