

A047229


Numbers that are congruent to {0, 2, 3, 4} mod 6.


15



0, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84
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OFFSET

1,2


COMMENTS

Appears to be the sequence of n such that n never divides 3^x2^x for x>=0.  Benoit Cloitre, Aug 19 2002
Numbers divisible by 2 or 3.  Nick Hobson (nickh(AT)qbyte.org), Mar 13 2007
Numbers k such that average of squares of the first k positive integers is not integer. A089128(a(n)) > 1. For n >= 2, a(n) = complement of A007310.  Jaroslav Krizek, May 28 2010
Numbers k such that k*Fibonacci(k) is even.  Gary Detlefs, Oct 27 2011
Also numbers that have a divisor d with 2^1 <= d < 2^2 (see Ei definition p. 340 in Besicovitch article).  Michel Marcus, Oct 31 2013
Starting with 0, 2, a(n) is the smallest number greater than a(n1) that is not relatively prime to a(n2).  Franklin T. AdamsWatters, Dec 04 2014


LINKS



FORMULA

a(n) = (1/8)*(11*((n1) mod 4) + (n mod 4) + ((n+1) mod 4)  ((n+2) mod 4)) + 6*A002265(n1).  Paolo P. Lava, Nov 05 2007
a(n) = (6*(n1)  (1+(1)^n)*(1)^(n*(1+(1)^n)/4))/4; also a(n) = (6*(n1)  (i)^n  i^n)/4, where i is the imaginary unit.  Bruno Berselli, Nov 08 2010
G.f.: x^2*(2x+2*x^2) / ( (x^2+1)*(x1)^2 ).  R. J. Mathar, Oct 08 2011
a(n) = a(n1) + a(n4)  a(n5), n>4.  Gionata Neri, Apr 15 2015
a(n) = n + 2*floor((n2)/4) + floor(f(n+2)/3), where f(n) = n mod 4.  Aleksey A. Solomein, Feb 08 2016
Sum_{n>=2} (1)^n/a(n) = log(3)/2  log(2)/3.  Amiram Eldar, Dec 12 2021


MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 2, 3, 4}, Mod[#, 6]]&] (* Harvey P. Dale, Aug 15 2011 *)
a[ n_] := With[ {m = n  1}, {2, 3, 4, 0}[[Mod[m, 4, 1]]] + Quotient[ m, 4] 6]; (* Michael Somos, Oct 05 2015 *)


PROG

(Magma) [ n : n in [0..150]  n mod 6 in [0, 2, 3, 4]] ; // Vincenzo Librandi, Jun 01 2011
(Haskell)
a047229 n = a047229_list !! (n1)
a047229_list = filter ((`notElem` [1, 5]) . (`mod` 6)) [0..]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



