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A066488
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Composite numbers k which divide A001045(k-1).
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2
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341, 1105, 1387, 1729, 2047, 2465, 2701, 2821, 3277, 4033, 4369, 4681, 5461, 6601, 7957, 8321, 8911, 10261, 10585, 11305, 13741, 13747, 13981, 14491, 15709, 15841, 16705, 18721, 19951, 23377, 29341, 30121, 30889, 31417, 31609, 31621, 34945
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OFFSET
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1,1
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COMMENTS
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Also composite numbers k such that (2^k - 2)/3 + 1 == 2^k - 1 == 1 (mod k).
An equivalent definition of this sequence: pseudoprimes to base 2 that are not divisible by 3. - Arkadiusz Wesolowski, Nov 15 2011
Conjecture: these are composites k such that 2^M(k-1) == -1 (mod M(k)^2 + M(k) + 1), where M(k) = 2^k - 1. - Amiram Eldar and Thomas Ordowski, Dec 19 2019
These are composites k such that 2^(m-1) == 1 (mod (m+1)^6 - 1), where m = 2^k - 1. - Thomas Ordowski, Sep 17 2023
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LINKS
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MATHEMATICA
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a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + 2a[n - 2]; Select[ Range[50000], IntegerQ[a[ # - 1]/ # ] && !PrimeQ[ # ] && # != 1 & ]
fQ[n_] := ! PrimeQ@ n && Mod[((2^n - 2)/3 + 1), n] == Mod[2^n - 1, n] == 1; Select[ Range@ 35000, fQ]
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PROG
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(Magma) [k:k in [4..40000]|not IsPrime(k) and ((2^(k-1) + (-1)^k) div 3) mod k eq 0]; // Marius A. Burtea, Dec 20 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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