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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

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

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Last modified June 21 23:16 EDT 2018. Contains 305646 sequences. (Running on oeis4.)