

A047211


Numbers that are congruent to {2, 4} mod 5.


27



2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 27, 29, 32, 34, 37, 39, 42, 44, 47, 49, 52, 54, 57, 59, 62, 64, 67, 69, 72, 74, 77, 79, 82, 84, 87, 89, 92, 94, 97, 99, 102, 104, 107, 109, 112, 114, 117, 119, 122, 124, 127, 129, 132, 134, 137, 139, 142, 144, 147, 149, 152, 154, 157, 159, 162, 164, 167, 169, 172, 174, 177, 179, 182, 184
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OFFSET

1,1


COMMENTS

Conjecture: n such that the characteristic polynomial of M(n) is irreducible over the rationals where M(n) is an n X n matrix with ones on the skew diagonal and below it and the skew line two positions above it and otherwise zeros; see example for one such matrix. Tested up to n=177.  Joerg Arndt, Aug 10 2011


LINKS

Table of n, a(n) for n=1..74.
Index entries for linear recurrences with constant coefficients, signature (1,1,1).


FORMULA

a(n) = a(n1) +a(n2) a(n3).
a(n) = (10*n3(1)^n)/4, (n>=1). [Corrected by Bruno Berselli, Sep 20 2010]
a(n) = 5*floor((n1)/2) +3 +(1)^n.  Gary Detlefs, Mar 02 2010
G.f.: x*(2+2*x+x^2)/((1+x)*(1x)^2).  Paul Barry, Sep 11 2008
a(n) = 5*na(n1)4 (with a(1)=2).  Vincenzo Librandi, Nov 18 2010
a(n) = floor((5*n1)/2).  Gary Detlefs, May 14 2011
a(n) = 2*n + floor((n1)/2).  Arkadiusz Wesolowski, Sep 19 2012


EXAMPLE

The 7 X 7 matrix (dots for zeros):
[....1.1]
[...1.11]
[..1.111]
[.1.1111]
[1.11111]
[.111111]
[1111111]
has the characteristic polynomial x^7  5*x^6  4*x^5 + 15*x^4 + 5*x^3  11*x^2  x + 1 which is irreducible over the field of rational numbers, and 7 is a term of the sequence.  Joerg Arndt, Aug 10 2011


MAPLE

seq(5*floor((n1)/2) +3 +(1)^n, n=1..50); # Gary Detlefs, Mar 02 2010


MATHEMATICA

Select[Range[0, 200], MemberQ[{2, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)


PROG

(Haskell)
a047211 n = a047211_list !! (n1)
a047211_list = filter ((`elem` [2, 4]) . (`mod` 5)) [1..]
 Reinhard Zumkeller, Oct 03 2012
(MAGMA) [Floor((5*n1)/2): n in [1..50]]; // Wesley Ivan Hurt, May 25 2014
(PARI) a(n)=(5*n1)\2 \\ Charles R Greathouse IV, Sep 24 2015


CROSSREFS

Cf. A047209.
Cf. A053685 (subsequence).
Sequence in context: A022840 A064995 A067839 * A225000 A189677 A087733
Adjacent sequences: A047208 A047209 A047210 * A047212 A047213 A047214


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 11 1999


EXTENSIONS

Conjecture corrected by John M. Campbell, Aug 25 2011


STATUS

approved



