0,2

a(n)/n -> 10^n/(2*n). [Corrected by Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007]

C. L. Mallows, Conway's challenge sequence, Amer. Math. Monthly, 98 (1991), 5-20. See comments on formula due to G. Phillips on page 18

Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007, Table of n, a(n) for n = 0..30

a[1] = a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; Do[ a[n], {n, 1000000}]; Table[ a[10^n], {n, 0, 6}]

(PARI) print1("1, "); for(k=1, 30, n=10^k; row=floor(log(n)/log(2)); col=1; s=0; a=0; while(s<n, for(j=col, row+1, if(j>1, smd=binomial(row, j-2), smd=2^row); if((s+smd)>n, col=j-1; row=row-1; break, s+=smd; if(j>1, a+=binomial(row-1, j-2), a+=2^(row-1))))); print1(a", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007

Cf. A004001.

Sequence in context: A083696 A001593 A124546 this_sequence A138414 A130565 A124556

Adjacent sequences: A095897 A095898 A095899 this_sequence A095901 A095902 A095903

nonn

Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 11 2004

2 more terms from Ryan Propper (rpropper(AT)stanford.edu), Jan 05 2007

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007