|
| |
|
|
A047566
|
|
Numbers that are congruent to {4, 5, 6, 7} mod 8.
|
|
9
|
|
|
|
4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31, 36, 37, 38, 39, 44, 45, 46, 47, 52, 53, 54, 55, 60, 61, 62, 63, 68, 69, 70, 71, 76, 77, 78, 79, 84, 85, 86, 87, 92, 93, 94, 95, 100, 101, 102, 103, 108, 109
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Numbers having a 1 in position 2 of their binary expansion. One of the mystery calculator sequences: A005408, A042964, A047566, A115419, A115420, A115421. - Jeremy Gardiner, Jan 22 2006
|
|
|
LINKS
|
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Maths Magic, Mystery Calculator.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
|
|
|
FORMULA
|
a(n) = (1/3)*{5*(n mod 4)+2*[(n+1) mod 4]+2*[(n+2) mod 4]+2*[(n+3) mod 4]} + 8*A002265. - Paolo P. Lava, Feb 15 2008
G.f.: x*(4+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 19 2016: (Start)
a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.
a(n) = (4*n+1-(-1)^n-(-1)^((n+1)/2)-(-1)^(n/2)-(-1)^(-(n+1)/2)-(-1)^(-n/2))/2. (End)
E.g.f.: 1 + sin(x) - cos(x) + sinh(x) + 2*x*exp(x). - Ilya Gutkovskiy, May 20 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16 - 3*log(2)/8. - Amiram Eldar, Dec 26 2021
|
|
|
MAPLE
|
A047566:= n-> n+3 + 4*iquo(n-1, 4):
seq(A047566(n), n=1..100); # Alois P. Heinz, Aug 22 2011
|
|
|
MATHEMATICA
|
Flatten[# + {4, 5, 6, 7}&/@(8Range[0, 14])] (* Harvey P. Dale, Feb 02 2011 *)
|
|
|
PROG
|
(Haskell)
a047566 n = a047566_list !! (n-1)
a047566_list = [n | n <- [1..], mod n 8 > 3]
-- Reinhard Zumkeller, Dec 29 2012
|
|
|
CROSSREFS
|
Cf. A002265, A003628 (primes).
Mystery calculator sequences: A005408, A042964, A047566, A115419, A115420, A115421.
Sequence in context: A014098 A086101 A131260 * A283775 A037355 A294228
Adjacent sequences: A047563 A047564 A047565 * A047567 A047568 A047569
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
