OFFSET
0,2
LINKS
H. Zantema, Minimizing sums of addition chains, RUU-CS-89-15 (1989).
H. Zantema, Minimizing sums of addition chains, J. Algorithms 12 (1991) 281-307.
EXAMPLE
The smallest chain for 5 is 2, 3, 5 with sum a(2) = 2+3+5 = 10.
the smallest chain for 7 is 2, 3, 4, 7 with sum a(3) = 2+3+4+7 = 16.
PROG
(PARI) step(V)=my(U=List(), v); for(i=1, #V, v=V[i]; for(i=1, #v, for(j=i, #v, if(v[i]+v[j]>v[#v], listput(U, concat(v, v[i]+v[j])))))); vecsort(Vec(U), , 8)
sm(v)=sum(i=2, #v, v[i])
a(n)=if(n<2, return(5*n)); n=2*n+1; my(V=[[1, 2]], U, t); while(#(U=select(v->v[#v]==n, V))==0, V=select(v->v[#v]<=n, step(V))); t=vecmin(apply(sm, U)); while(#V, V=step(select(v->sm(v)<t-n, V)); for(i=1, #V, my(v=V[i]); if(v[#v]==n, t=min(sm(v), t)))); t \\ Charles R Greathouse IV, Jul 17 2013
CROSSREFS
KEYWORD
nonn,nice,more
AUTHOR
N. J. A. Sloane, Aug 07 2003
EXTENSIONS
a(30)-a(46) from Sean A. Irvine, Mar 08 2018
STATUS
approved