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A060121
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First solution mod p of x^3 = 2 for primes p such that only one solution exists.
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6
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0, 2, 3, 7, 8, 16, 26, 5, 21, 18, 38, 49, 50, 16, 26, 6, 81, 54, 98, 70, 157, 161, 58, 147, 21, 86, 92, 197, 50, 249, 137, 184, 119, 45, 45, 261, 198, 61, 176, 143, 51, 103, 221, 72, 11, 219, 35, 86, 385, 384, 141, 143, 225, 92, 245, 533, 557, 473, 170, 375, 516
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Solutions mod p are represented by integers from 0 to p-1. For i > 1, i is a solution mod p of x^3 = 2 iff p is a prime factor of i^3-2 and p > i (cf. comment to A059940). i^3-2 has at most two prime factors > i. Hence i is a solution mod p of x^3 = 2 for at most two different p and therefore no integer occurs more than twice in this sequence. There are integers which do occur twice, e.g. 16, 21, 26 (cf. A060914). Moreover, no integer occurs more than twice in A060121, A060122, A060123 and A060124 taken together.
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FORMULA
| a(n) = first (only) solution mod p of x^3 = 2, where p is the n-th prime such that x^3 = 2 has only one solution mod p, i.e. p is the n-th term of A045309.
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EXAMPLE
| a(9) = 21, since 47 is the ninth term of A045309 and 21 is the only solution mod 47 of x^3 = 2.
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CROSSREFS
| Cf. A040028, A045309, A059940, A060914, A060122, A060123, A060124.
Sequence in context: A101755 A076550 A062269 * A002964 A166966 A181658
Adjacent sequences: A060118 A060119 A060120 * A060122 A060123 A060124
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KEYWORD
| nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 02 2001
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