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A047530
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Numbers that are congruent to {0, 1, 3, 7} mod 8.
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3
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0, 1, 3, 7, 8, 9, 11, 15, 16, 17, 19, 23, 24, 25, 27, 31, 32, 33, 35, 39, 40, 41, 43, 47, 48, 49, 51, 55, 56, 57, 59, 63, 64, 65, 67, 71, 72, 73, 75, 79, 80, 81, 83, 87, 88, 89, 91, 95, 96, 97, 99, 103, 104, 105, 107
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Numbers n such that the n-th homotopy group of the topological group O(oo) does not vanish [see Baez]. Cf. A195679.
The a(n+1) determine the maximal number of linearly independent smooth nowhere zero vector fields on a (2n+1)-sphere, see A053381. [Johannes W. Meijer, Jun 07 2011]
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REFERENCES
| J. C. Baez, The octonions, Bull. Amer. Math. Soc., 39 (2002), 145-205.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (1,0,0,1,-1).
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FORMULA
| From Johannes W. Meijer, Jun 07 2011: (Start)
a(n) = ceil(n/4) + 2*ceil((n-1)/4) + 4*ceil((n-2)/4) + ceil((n-3)/4)
a(n+1) = A053381(2^p) (End)
G.f. x^2*(1+2*x+4*x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
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MAPLE
| A047530 := proc(n): ceil(n/4) + 2*ceil((n-1)/4) + 4*ceil((n-2)/4) + ceil((n-3)/4) end: seq(A047530(n), n=0..47); [Johannes W. Meijer, Jun 07 2011]
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PROG
| (PARI) a(n)=n>>2<<3+[-1, 0, 1, 3][n%4+1] \\ Charles R Greathouse IV, Jun 09 2011
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CROSSREFS
| Cf. A008621 [Johannes W. Meijer, Jun 07 2011]
Sequence in context: A091679 A116034 A122987 * A096315 A112680 A096079
Adjacent sequences: A047527 A047528 A047529 * A047531 A047532 A047533
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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