

A065903


Integers i > 1 for which there is no prime p such that i is a solution mod p of x^4 = 2.


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
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OFFSET

1,1


COMMENTS

Solutions mod p are represented by integers from 0 to p1. 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.


LINKS

Table of n, a(n) for n=1..37.


FORMULA

a(n) = nth 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).


PROG

(PARI): a065903(m) = local(c, n, f, a); c = 0; n = 2; while(c<m, f = factor(n^42); 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: A263061 A281062 A020241 * A204488 A062680 A251291
Adjacent sequences: A065900 A065901 A065902 * A065904 A065905 A065906


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Nov 28 2001


STATUS

approved



