|
| |
|
|
A007675
|
|
Numbers n such that n, n+1 and n+2 are squarefree.
(Formerly M3824)
|
|
11
| |
|
|
1, 5, 13, 21, 29, 33, 37, 41, 57, 65, 69, 77, 85, 93, 101, 105, 109, 113, 129, 137, 141, 157, 165, 177, 181, 185, 193, 201, 209, 213, 217, 221, 229, 237, 253, 257, 265, 281, 285, 301, 309, 317, 321, 329, 345
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| There can not be four consecutive squarefree numbers as one of them is divisible by 2^2 =4. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 18 2002
|
|
|
REFERENCES
| P. R. Halmos, Problems for Mathematicians Young and Old. Math. Assoc. America, 1991, p. 28.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
|
|
|
FORMULA
| m(x)*m(x+1)*m(x+2)=1, where m(w)=Abs(mu(w)). - Labos E. (labos(AT)ana.sote.hu)
|
|
|
EXAMPLE
| 4 categories: all terms are composites like {33,34,35}; first term only is prime like {37,38,39}; 3rd term only is prime like {57,58,59}; first and 3rd are primes like {29,30,31}. - Labos E. (labos(AT)ana.sote.hu)
85 is a term as 85 = 17*5, 86 = 43*2, 87 = 29*3.
|
|
|
MATHEMATICA
| Select[Range[1000], SquareFreeQ[#(#+1)(#+2)]&] (*From Vladimir Joseph Stephan Orlovsky, Mar 30 2011*)
|
|
|
PROG
| (Haskell)
a007675 n = a007675_list !! (n-1)
a007675_list = f 1 a008966_list where
f n (u:xs'@(v:w:x:xs)) | u == 1 && w == 1 && v == 1 = n : f (n+4) xs
| otherwise = f (n+1) xs'
-- Reinhard Zumkeller, Nov 05 2011
|
|
|
CROSSREFS
| Cf. A005117, A013929.
Cf. A008966.
Sequence in context: A184837 A197120 A030374 * A043441 A004770 A191155
Adjacent sequences: A007672 A007673 A007674 * A007676 A007677 A007678
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
|
| |
|
|
