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A065912 Fourth solution mod p of x^4 = 2 for primes p such that more than two solution exists. 5
55, 84, 86, 205, 222, 235, 206, 305, 325, 489, 556, 494, 830, 928, 964, 972, 1046, 976, 721, 940, 1162, 1132, 1065, 871, 1469, 1289, 1328, 1477, 1594, 1253, 1760, 1604, 1782, 1877, 1883, 1442, 2002, 2114, 2144, 1709, 2112, 1909, 2277, 2343, 2492, 2735 (list; graph; refs; listen; history; text; internal format)
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
FORMULA
a(n) = fourth 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) = 86, since 113 is the third term of A014754, 27, 47, 66 and 86 are the solutions mod 113 of x^4 = 2 and 86 is the fourth one.
PROG
(PARI): a065912(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]>3, print1(s[4], ", "))) a065912(3000)
CROSSREFS
Sequence in context: A119224 A135984 A140377 * A245284 A203613 A366848
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Nov 29 2001
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)