|
Search: id:A065912
|
|
|
| A065912 |
|
Fourth solution mod p of x^4 = 2 for primes p such that more than two solution exists. |
|
+0
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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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).
|
|
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.
|
|
PROGRAM
|
(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
|
Cf. A040098, A007522, A014754, A065909, A065910, A065911.
Sequence in context: A119224 A135984 A140377 this_sequence A039533 A157484 A027865
Adjacent sequences: A065909 A065910 A065911 this_sequence A065913 A065914 A065915
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 29 2001
|
|
|
Search completed in 0.002 seconds
|
