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Search: id:A122780
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| A122780 |
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Nonprimes n such that 3^n==3 (mod n). |
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+0
8
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| 1, 6, 66, 91, 121, 286, 561, 671, 703, 726, 949, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4961, 5551, 6601, 7107, 7381, 8205, 8401, 8646, 8911, 10585, 11011, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345
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OFFSET
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1,2
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COMMENT
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Theorem: If q!=3 and both numbers q and (2q-1) are primes then n=q*(2q-1) is in the sequence. 6, 91, 703, 1891, 2701, 12403, 18721, 38503, 49141, ... is the related subsequence.
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EXAMPLE
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66 is composite and 3^66=66*468229611858069884271524875811+3 so 66 is in the sequence.
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MATHEMATICA
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Select[Range[30000], ! PrimeQ[ # ] && Mod[3^#, # ] == Mod[3, # ] &]
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CROSSREFS
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Cf. A001567, A122014, A122781-9.
Sequence in context: A137121 A110222 A119230 this_sequence A153514 A119144 A153087
Adjacent sequences: A122777 A122778 A122779 this_sequence A122781 A122782 A122783
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KEYWORD
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easy,nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 11 2006
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