|
Search: id:A065903
|
|
|
| A065903 |
|
Integers i > 1 for which there is no prime p such that i is a solution mod p of x^4 = 2. |
|
+0
6
|
|
| 1689, 1741, 3306, 3894, 4362, 4587, 4999, 5754, 6025, 6371, 6668, 7012, 7982, 9054, 9158, 9695, 9742, 9832, 10056, 10664, 11005, 12027, 12385, 13676, 13895, 14026, 14059, 16104, 16239, 16903, 17050, 17153, 18079, 18202, 18642, 20349, 21060
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Solutions mod p are represented by integers from 0 to p-1. The following equivalences holds for i > 1: There is a prime p such that i is a solution mod p of x^4 = 2 iff i^4 - 2 has a prime factor > i; i is a solution mod p of x^4 = 2 iff p is a prime factor of i^4 - 2 and p > i. i^4 - 2 has at most three prime factors > i. For i such that i^4 - 2 has one resp. two resp. three prime factors > i; cf. A065904 resp. A065905 resp. A065906.
|
|
FORMULA
|
a(n) = n-th integer i such that i^4 - 2 has no prime factor > i.
|
|
EXAMPLE
|
a(2) = 1741, since 1741 is (after 1689) the second integer i for which there are no primes p > i such that i is a solution mod p of x^4 = 2, or equivalently, 1741^4 - 2 = 9187452028559 = 7*7*79*887*1609*1663 has no prime factor > 1741. (cf. A065902).
|
|
PROGRAM
|
(PARI): a065903(m) = local(c, n, f, a); c = 0; n = 2; while(c<m, f = factor(n^4-2); a = matsize(f)[1]; if(f[a, 1]< = n, print1(n, ", "); c++); n++) a065903(40)
|
|
CROSSREFS
|
Cf. A040028, A065902, A065904, A065905, A065906.
Sequence in context: A031539 A031719 A020241 this_sequence A062680 A120564 A089674
Adjacent sequences: A065900 A065901 A065902 this_sequence A065904 A065905 A065906
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 28 2001
|
|
|
Search completed in 0.002 seconds
|
