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A038509
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Composite numbers congruent to +-1 mod 6.
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47
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25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119, 121, 125, 133, 143, 145, 155, 161, 169, 175, 185, 187, 203, 205, 209, 215, 217, 221, 235, 245, 247, 253, 259, 265, 275, 287, 289, 295, 299, 301, 305, 319, 323, 325, 329, 335, 341, 343, 355, 361, 365, 371, 377, 385
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OFFSET
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1,1
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COMMENTS
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Or, composite numbers with smallest prime factor >= 5.
Or, nonprime numbers n such that binomial(n+3, 3) mod n == 1. - Hieronymus Fischer, Sep 30 2007
Note that the primes > 3 are congruent to +-1 mod 6.
This sequence differs from A067793 (composite n such that phi(n) > 2n/3) starting at 385. Numbers in this sequence but not in A067793 are 385, 455, 595, 665, 805, 1015, 1085, 1925, 2275, 2695, etc. See A069043. - R. J. Mathar, Jun 08 2008 and Zak Seidov, Nov 02 2011
The product (24/25) * (36/35) * (48/49) * (54/55) * (66/65) * (78/77) * (84/85) * (90/91) * ... * ((6*k)/a(n)) * ... = Pi^2/(6*sqrt(3)), where 6*k is the nearest number to a(n), with k in A067611 but not in A002822. (See A258414.) - Dimitris Valianatos, Mar 27 2017
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LINKS
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FORMULA
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MAPLE
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option remember;
if n = 1 then
25;
else
for a from procname(n-1)+1 do
if not isprime(a) and modp(a, 6) in {1, 5} then
return a;
end if;
end do:
end if;
end proc:
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MATHEMATICA
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Select[Range[1000], FactorInteger[#][[1, 1]] >= 5 && ! PrimeQ[#] &] (* Robert G. Wilson v, Dec 19 2009 *)
With[{nn=400}, Select[Rest[Complement[Range[nn], Prime[Range[ PrimePi[ nn]]]]], MemberQ[ {1, 5}, Mod[#, 6]]&]] (* Harvey P. Dale, Feb 21 2013 *)
Select[Range[400], CompositeQ[#]&&MemberQ[{1, 5}, Mod[#, 6]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 13 2019 *)
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PROG
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(Haskell)
a038509 n = a038509_list !! (n-1)
a038509_list = [x | x <- a002808_list, gcd x 6 == 1]
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CROSSREFS
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Cf. A171993 (nonprimes of the form 3*k+-1).
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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