

A065907


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


3



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


LINKS

Table of n, a(n) for n=1..60.


FORMULA

a(n) = first (least) solution mod p of x^4 = 2, where p is the nth prime such that x^4 = 2 has only two solutions mod p, i.e. p is the nth term of A007522.


EXAMPLE

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


PROG

(PARI): a065907(m) = local(s); forprime(p = 2, m, s = []; for(x = 0, p1, if(x^4%p == 2%p, s = concat(s, [x]))); if(matsize(s)[2] == 2, print1(s[1], ", "))) a065907(1600)


CROSSREFS

Cf. A040098, A007522, A065908.
Sequence in context: A059449 A272930 A140973 * A031272 A277139 A213082
Adjacent sequences: A065904 A065905 A065906 * A065908 A065909 A065910


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Nov 29 2001


STATUS

approved



