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Search: id:A065911
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| A065911 |
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Third 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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| 48, 81, 66, 162, 211, 190, 179, 251, 299, 299, 385, 416, 526, 827, 736, 766, 936, 586, 703, 779, 639, 999, 980, 808, 1137, 975, 1314, 1458, 1557, 1112, 1041, 1563, 1415, 1150, 1681, 1355, 1723, 1623, 1468, 1303, 1398, 1702, 2265, 1958, 1787, 2668, 2000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: no integer occurs more than three time in this sequence. Confirmed for the first 1182 terms of A014754 (primes < 100000). In this section, there are no integers which do occur thrice. 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
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a(n) = third 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
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a(3) = 66, since 113 is the third term of A014754, 27, 47, 66 and 86 are the solutions mod 113 of x^4 = 2, and 66 is the third one.
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PROGRAM
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(PARI): a065911(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[3], ", "))) a065911(3000)
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CROSSREFS
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Cf. A040098, A007522, A014754, A065909, A065910, A065912.
Sequence in context: A110229 A108608 A030628 this_sequence A039426 A043249 A044029
Adjacent sequences: A065908 A065909 A065910 this_sequence A065912 A065913 A065914
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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), Nov 29 2001
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