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A065908
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Second solution mod p of x^4 = 2 for primes p such that only two solutions exist.
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3
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5, 15, 16, 30, 56, 76, 55, 123, 135, 133, 158, 152, 125, 147, 195, 208, 197, 281, 214, 226, 324, 403, 307, 364, 401, 445, 377, 310, 574, 641, 701, 492, 677, 609, 602, 444, 636, 854, 791, 511, 599, 852, 690, 623, 786, 914, 769, 698, 692, 1102, 1201, 1073
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: no integer occurs more than three times in this sequence. Confirmed for the first 2399 terms of A007522 (primes < 100000). In this section, there are no integers which do occur thrice.
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FORMULA
| a(n) = second (largest) solution mod p of x^4 = 2, where p is the n-th prime such that x^4 = 2 has only two solutions mod p, i.e. p is the n-th term of A007522.
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EXAMPLE
| a(3) = 16, since 31 is the third term of A007522 and 16 is the second solution mod 31 of x^4 = 2.
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PROG
| (PARI): a065908(m) = local(s); forprime(p = 2, m, s = []; for(x = 0, p-1, if(x^4%p == 2%p, s = concat(s, [x]))); if(matsize(s)[2] == 2, print1(s[2], ", "))) a065908(1400)
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CROSSREFS
| A040098, A007522, A065907.
Sequence in context: A030486 A101238 A109161 * A166503 A134453 A174598
Adjacent sequences: A065905 A065906 A065907 * A065909 A065910 A065911
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KEYWORD
| nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 29 2001
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