A384482 Number of functions f(x) = b*x+c with nonnegative integer coefficients and a shortest addition-composition chain of length n, starting with 1 and x.
2, 3, 7, 20, 75, 412, 3200, 34167, 507344
Offset: 0
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The smallest n for which a(n) < A003313(n) is n = 21. The length of a shortest addition chain for 21 is A003313(21) = 6, but there are addition-composition chains of length 5, for example (1, x,) x+1, 2*x+2, 3*x+3, 6, 21. 6 and 21 are the compositions of 3*x+3 with 1 and 6, respectively.
n | functions b*x+c with b+c = a(n) and shortest chain of length n --+--------------------------------------------------------------- 0 | 1, x 1 | 2, x+1, 2*x 2 | 3, x+2, 2*x+1, 3*x 3 | 3+x, x+3 4 | 5+x, x+5 5 | 7+x, x+7 6 | 11*x+2 7 | 23*x+1 8 | 7*x+39, 43*x+3 9 | 11*x+87
Comments