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 A066488 Composite numbers n which divide A001045(n-1). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also composite numbers n such that ((2^n - 2)/3 + 1) == 2^n - 1 == 1 (mod n). An equivalent definition of this sequence: pseudoprimes to base 2 that are not divisible by 3. - Arkadiusz Wesolowski, Nov 15 2011 Conjecture: these are composite numbers n such that 2^M(n-1) == -1 (mod M(n)^2 + M(n) + 1), where M(n) = 2^n - 1. - Amiram Eldar and Thomas Ordowski, Dec 19 2019 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 MATHEMATICA 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] PROG (PARI) is(n)=n%3 && Mod(2, n)^(n-1)==1 && !isprime(n) && n>1 \\ Charles R Greathouse IV, Sep 18 2013 (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 CROSSREFS Cf. A001045, A066047. Sequence in context: A172255 A087835 A271221 * A291601 A083876 A068216 Adjacent sequences:  A066485 A066486 A066487 * A066489 A066490 A066491 KEYWORD easy,nonn AUTHOR Robert G. Wilson v, Jan 03 2002 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)