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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 (list; graph; refs; listen; history; text; internal format)
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 to sequences with linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = a(n-1) +a(n-2) -a(n-3).

a(n) = (10*n-3-(-1)^n)/4, (n>=1). [Corrected by Bruno Berselli, Sep 20 2010]

a(n) = 5*floor((n-1)/2) +3 +(-1)^n. [From Gary Detlefs, Mar 02 2010]

G.f.: x*(2+2*x+x^2)/((1+x)*(1-x)^2); [From Paul Barry, Sep 11 2008]

a(n) = 5*n-a(n-1)-4 (with a(1)=2). [From Vincenzo Librandi, Nov 18 2010]

a(n) = floor((5*n-1)/2). [From Gary Detlefs, May 14 2011]

a(n) = 2*n + floor((n-1)/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((n-1)/2) +3 +(-1)^n, n= 1..50); [From 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 !! (n-1)

a047211_list = filter ((`elem` [2, 4]) . (`mod` 5)) [1..]

-- Reinhard Zumkeller, Oct 03 2012

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.

EXTENSIONS

Conjecture corrected by John M. Campbell, Aug 25 2011.

STATUS

approved

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Last modified April 25 00:50 EDT 2014. Contains 240991 sequences.