A095900 a(n) = A004001(10^n).

1, 6, 57, 510, 5373, 53505, 510403, 5247173, 52736107, 511172800, 5189628970, 52334438874, 511861449132, 5150236044255, 52074775905991, 512279427101305, 5118687220533539, 51879201305335167, 512519244788358058

Offset: 0

Author

Robert G. Wilson v, Jun 11 2004

Keywords

• nonn

Comments

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

Links

• Herman Jamke, Table of n, a(n) for n = 0..30
• 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.

Crossrefs

Cf. A004001.

Programs

Mathematica

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(s1,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

Extensions

2 more terms from Ryan Propper, Jan 05 2007

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