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Search: id:A060914
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| A060914 |
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Integers i > 1 for which there are two primes p such that i is a solution mod p of x^3 = 2. |
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6
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| 7, 16, 20, 21, 26, 32, 34, 45, 49, 50, 52, 54, 57, 58, 61, 70, 72, 79, 81, 86, 92, 94, 98, 103, 111, 112, 114, 116, 119, 122, 125, 130, 136, 137, 141, 143, 147, 152, 157, 160, 170, 176, 179, 181, 184, 186, 197, 198, 199, 214, 221, 222, 225, 231, 234, 236, 240
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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^3 = 2 iff i^3 - 2 has a prime factor > i; i is a solution mod p of x^3 = 2 iff p is a prime factor of i^3 - 2 and p > i. i^3 - 2 has at most two prime factors > i. For i such that i^3 - 2 has no prime factors > i; cf. A060591.
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FORMULA
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a(n) = n-th integer i such that i^3 - 2 has two prime factors > i.
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EXAMPLE
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a(3) = 20, since 20 is (after 7 and 16) the third integer i for which there are two primes p > i (viz. 31 and 43) such that i is a solution mod p of x^3 = 2, or equivalently, 20^3 - 2 = 7998 = 2*3*31*43 has two prime factors > 20. (cf. A059940).
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CROSSREFS
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A040028, A059940, A060591.
Sequence in context: A132348 A101073 A026226 this_sequence A044059 A044440 A114556
Adjacent sequences: A060911 A060912 A060913 this_sequence A060915 A060916 A060917
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 08 2001
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