

A038509


Composite numbers congruent to +1 mod 6.


41



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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
Intersection of A002808 and A007310.  Reinhard Zumkeller, Jun 30 2012
Composite numbers in A038179.  Paolo P. Lava, Oct 29 2015
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


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

a(n) ~ 3n.  Charles R Greathouse IV, Nov 20 2012


MATHEMATICA

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 *)


PROG

(Haskell)
a038509 n = a038509_list !! (n1)
a038509_list = [x  x < a002808_list, gcd x 6 == 1]
 Reinhard Zumkeller, Aug 05 2014, Jun 30 2012
(PARI) is(n)=gcd(n, 6)==1 && !isprime(n) && n>7 \\ Charles R Greathouse IV, Nov 20 2012


CROSSREFS

Cf. A171993 (nonprimes of the form 3*k+1).
Cf. A000040, A133620A133625, A133630, A133634A133636.
Cf. A133873, A133883, A133880, A133890, A133900, A133910.
Cf. A069043, A067793 (composite n such that phi(n) > 2n/3).
Sequence in context: A049514 A049518 A133633 * A067793 A287918 A054550
Adjacent sequences: A038506 A038507 A038508 * A038510 A038511 A038512


KEYWORD

nonn,nice


AUTHOR

Jeff Burch


EXTENSIONS

More terms from Robert G. Wilson v, Dec 19 2009
Entry revised by N. J. A. Sloane, Dec 31 2011, at the suggestion of Gary Detlefs


STATUS

approved



