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Search: id:A133154
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| A133154 |
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For the n-th prime p, a(n) is the smallest m<=p-1 such that there does not exist a value of j with 1<=j<=2p, except j=p-1, for which m^j+j==0 (mod p). |
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+0
1
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| 0, 0, 0, 2, 7, 11, 2, 5, 3, 8, 5, 26, 2, 2, 9, 16, 6, 14, 9, 9, 3, 10, 3, 10, 4, 2, 5, 2, 13, 2, 3, 2, 3, 21, 8, 22, 2, 3, 2, 5, 5, 2, 3, 2, 4, 2, 2, 7, 44, 7, 16, 3, 4, 3, 2, 19, 22, 3, 3, 26, 7, 16, 12, 2, 9, 6, 2, 14, 3, 4, 9, 6, 4, 19, 15, 6, 4, 6, 16, 5, 11, 9, 5, 4, 2, 3, 18, 3, 7, 9, 18, 16, 3, 8
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Andrew Granville, based on submitter's analysis of the data in A131685, made the following conjecture: "For some n with 1<=n<=p-1 there does not exist a value of j, with 1 <= j <= 2p, other than j=p-1, for which n^j+j == 0 mod p". Max Alekseyev's calculations confirm that the conjecture is true for the primes below 10^5. The sequence is made of the list of "first n", generated for each prime. a(n) = 0 means that there is no corresponding n, e.g. for p=2, 3 and 5.
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PROGRAM
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(PARI/GP program from Max Alekseyev, which he used to calculate first 100 values) { a(p) = for(n=1, p-1, local(j=1); while(j<=2*p, if( j!=p-1 && Mod(n, p)^j==-j, break); j++); if(j>2*p, return(n)); ); 0 } ? vector(100, n, a(prime(n)))
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CROSSREFS
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Cf. A131685.
Adjacent sequences: A133151 A133152 A133153 this_sequence A133155 A133156 A133157
Sequence in context: A015963 A056656 A110739 this_sequence A100020 A020638 A091385
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KEYWORD
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nonn
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AUTHOR
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Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 08 2007
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