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Search: id:A060515
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| A060515 |
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Integers i > 1 for which there is no prime p such that i is a solution mod p of x^2 = 2. |
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2
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| 2, 10, 28, 39, 45, 54, 58, 74, 87, 88, 101, 108, 114, 116, 130, 143, 147, 156, 164, 168, 178, 180, 181, 225, 228, 235, 238, 242, 244, 248, 256, 263, 270, 271, 277, 304, 305, 317, 318, 325, 333, 334, 338, 347, 363, 367, 373, 374, 378, 380, 381, 386, 397, 402
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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^2 = 2 iff i^2-2 has a prime factor > i; i is a solution mod p of x^2 = 2 iff p is a prime factor of i^2-2 and p > i.
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FORMULA
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Integer i > 1 is a term of this sequence iff i^2-2 has no prime factor > i.
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EXAMPLE
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a(1) = 2, since there is no prime p such that 2 is a solution mod p of x^2 = 2. a(2) = 10, since there is no prime p such that 10 is a solution mod p of x^2 = 2, and for each integer i from 3 to 9 there is a prime q such that i is a solution mod q of x^2 = 2 (cf. A059772).
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CROSSREFS
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A038873, A059772.
Sequence in context: A099583 A133479 A057753 this_sequence A109723 A053594 A006331
Adjacent sequences: A060512 A060513 A060514 this_sequence A060516 A060517 A060518
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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), Mar 24 2001
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