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Search: id:A130058
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| A130058 |
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a(n) = numbers n such that k=n*23^2 divides 3^(k-1) - 2^(k-1). |
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7
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| 1, 67, 89, 133, 199, 331, 617, 793, 881, 5281, 8911, 11419, 13333, 22177, 23585, 26467, 35113, 35839, 38897, 40657, 44023, 54913, 65869, 67849, 70819, 92929, 105469, 107185, 114247, 124279, 144673, 153253, 159259, 185329, 196945, 225589
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OFFSET
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1,2
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COMMENT
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All prime p>3 divide 3^(p-1) - 2^(p-1). It appears that 1 and 529 = 23^2 are the only perfect squares in A073631(n) = {1, 65, 133, 529, 793, 1105, 1649, 1729, ...} Nonprimes n such that n divides 3^(n-1)-2^(n-1). Most terms of A073631(n) are square-free. First 50 non-square-free terms of A073631(n) are the multiples of 23^2. Conjecture: All non-square-free terms of A073631(n) are the multiples of 23^2. Prime terms in a(n) are listed in A130059 = {67,89,199,331,617,881,5281,35839,...}. Note that the many terms in a(n) {1,133,793,8911,13333,22177,26467,38897,44023,54913,65869,...} are also in A073631(n).
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MATHEMATICA
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Do[ k=n*23^2; f=PowerMod[ 3, k-1, k ] - PowerMod[ 2, k-1, k ]; If[ IntegerQ[ f/k ], Print[ n ] ], {n, 1, 1000000} ]
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CROSSREFS
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Cf. A073631 = Nonprimes n such that n divides 3^(n-1) - 2^(n-1). Cf. A001047 = 3^n - 2^n. Cf. A130059.
Adjacent sequences: A130055 A130056 A130057 this_sequence A130059 A130060 A130061
Sequence in context: A091075 A139973 A118741 this_sequence A119893 A130059 A039539
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), May 04 2007
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