1,2

Consider the complementary equation b(n)=a(a(n))+n, with solutions

a=A136495 and b=A136496; let r = lim a(n)/n and s = lim b(n)/n. The

Beatty sequences of r and s are A138251 and A138252. We here introduce

the notion of Beatty discrepancy of a complementary equation so that,

in this case, it measures the closeness of the pair (A136495,A136496)

to the Beatty pair (A138251,A138252).

A138253(n) = d(n)-c(c(n))-n, where c(n)=A138251(n), d(n)=A138252(n).

d(1)-c(c(1))-1=3-1-1=1;

d(2)-c(c(2))-2=6-2-2=2;

d(3)-c(c(3))-3=9-5-3=1;

d(4)-c(c(4))-4=12-7-4=1.

Cf. A136495, A136496, A138251, A138252.

Sequence in context: A142598 A037800 A144411 this_sequence A085737 A005090 A073490

Adjacent sequences: A138250 A138251 A138252 this_sequence A138254 A138255 A138256

nonn

Clark Kimberling (ck6(AT)evansville.edu), Mar 09 2008