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A047211
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Numbers that are congruent to {2, 4} mod 5.
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21
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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; internal format)
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OFFSET
| 1,1
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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]
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FORMULA
| a(n) = +1*a(n-1) +1*a(n-2) -1*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]
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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]
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MAPLE
| seq(5*floor((n-1)/2) +3 +(-1)^n, n= 1..50); [From Gary Detlefs, Mar 02 2010]
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MATHEMATICA
| Select[Range[0, 200], MemberQ[{2, 4}, Mod[#, 5]] &] (* From Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)
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CROSSREFS
| Cf. A047209
Sequence in context: A022840 A064995 A067839 * A189677 A087733 A065027
Adjacent sequences: A047208 A047209 A047210 * A047212 A047213 A047214
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Conjecture corrected by John M. Campbell, Aug 25 2011.
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