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A065909
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First solution mod p of x^4 = 2 for primes p such that more than two solution exists.
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5
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18, 5, 27, 28, 35, 46, 131, 48, 252, 104, 45, 123, 51, 9, 69, 77, 51, 177, 472, 261, 55, 117, 224, 562, 12, 264, 273, 132, 127, 500, 17, 197, 107, 36, 206, 671, 127, 159, 137, 684, 329, 564, 316, 314, 197, 98, 661, 925, 461, 170, 930, 151, 1081, 333, 434, 924
(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 time in this sequence. Confirmed for the first 1182 terms of A014754 (primes < 100000). There are integers which do occur thrice, e.g. 6624. Moreover, no integer is first, second, third or fourth solution for more than three primes. Confirmed for the first 2399 terms of A007522 and the first 1182 terms of A014754 (primes < 100000).
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FORMULA
| a(n) = first (least) solution mod p of x^4 = 2, where p is the n-th prime such that x^4 = 2 has more than two solutions mod p, i.e. p is the n-th term of A014754.
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EXAMPLE
| a(3) = 27, since 113 is the third term of A014754, 27, 47, 66 and 86 are the solutions mod 113 of x^4 = 2 and 27 is the least one.
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PROG
| (PARI): a065909(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[1], ", "))) a065909(4000)
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CROSSREFS
| Cf. A040098, A007522, A014754, A065910, A065911, A065912.
Sequence in context: A040314 A160486 A040312 * A186158 A038642 A040311
Adjacent sequences: A065906 A065907 A065908 * A065910 A065911 A065912
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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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