A084351 - OEIS

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A084351

Length of period of sequences r(k,n)=floor(sin(1)*k!)-n*floor(sin(1)*k!/n) when n is fixed.

1, 4, 12, 4, 20, 12, 28, 8, 36, 20, 44, 12, 52, 28, 60, 16, 68, 36, 76, 20, 84, 44, 92, 24, 100, 52, 108, 28, 116, 60, 124, 32, 132, 68, 140, 36, 148, 76, 156, 40, 164, 84, 172, 44, 180, 92, 188, 48, 196, 100, 204, 52, 212, 108, 220, 56, 228, 116, 236, 60, 244, 124, 252

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..63.

FORMULA

For n>1 a(n)=n if n==0 (mod 4), a(n)=2n is n==0 (mod 2) and n is not divisible by 4, a(n)=4n if n is odd.

Empirical g.f.: x * (-3*x^8 +4*x^6 +4*x^5 +18*x^4 +4*x^3 +12*x^2 +4*x+1) / (x^8 -2*x^4 +1). - Colin Barker, Jun 16 2013

PROG

(PARI) a(n)=if(n<2, 1, if(n%2-1, if(n%4, 2*n, n), 4*n))

CROSSREFS

Cf. A084348.