0,3

The rightmost digit in the base-8 representation of n. Also, the equivalent value of the three rightmost digits in the base-2 representation of n. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 12 2007

a(n)=n mod 8. Complex representation: a(n)=1/8*(1-r^n)*sum{1<=k<8, k*product{1<=m<8,m<>k, (1-r^(n-m))}} where r=exp(pi/4*i)=(1+i)*sqrt(2)/2 and i=sqrt(-1). Trigonometric representation: a(n)=256*(sin(n*pi/8))^2*sum{1<=k<8, k*product{1<=m<8,m<>k, (sin((n-m)*pi/8))^2}}. G.f.: g(x)=(sum{1<=k<8, k*x^k})/(1-x^8). Also: g(x)=x(7x^8-8x^7+1)/((1-x^8)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007

a(n)=n mod 2+2*(floor(n/2)mod 4)=A000035(n)+2*A010873(A004526(n)). Also: a(n)=n mod 4+4*(floor(n/4)mod 2)=A010873(n)+4*A000035(A002265(n)). Also: a(n)=n mod 2+2*(floor(n/2)mod 2)+4*(floor(n/4)mod 2)=A000035(n)+2*A000035(A004526(n)))+4*A000035(A002265(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 12 2007

a(n)=(1/2)*(7-(-1)^n-2*(-1)^(b/4)-4*(-1)^((b-2+2*(-1)^(b/4))/8)) where b=2n-1+(-1)^n. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 12 2007

General formula for period 2^k: a(n)=(1/2)*(2^k-1-sum{0<=j<k, 2^j*(-1)^p(j,n)}) where p(j,n) is defined recursively by p(0,n)=n, p(j,n)=(1/4)*(2*p(j-1,n)-1+(-1)^p(j-1,n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 14 2007

Partial sums: A130486. Other related sequences A130481, A130482, A130483, A130484, A130485.

Cf. A010887, A130909.

Cf. A010873, A130909.

Adjacent sequences: A010874 A010875 A010876 this_sequence A010878 A010879 A010880

Sequence in context: A037850 A037886 A031045 this_sequence A004183 A031035 A054634

nonn

njas