A179852 Number of terms in the simple continued fraction for (e truncated to n decimal digits).

1, 4, 6, 8, 12, 13, 15, 17, 23, 24, 31, 23, 29, 29, 34, 38, 36, 42, 38, 47, 44, 44, 50, 48, 49, 54, 60, 56, 60, 61, 60, 60, 70, 68, 77, 72, 71, 82, 68, 81, 78, 83, 82, 82, 89, 91, 102, 90, 98, 99, 103, 97, 90, 107, 107, 112, 111, 120, 109, 115, 118, 112, 111, 127, 128, 133, 117, 117, 117, 139, 136

Offset: 1

Author

Umut Uludag, Jan 11 2011

Keywords

• nonn
• base
• less

Examples

			a(1): simple continued fraction (SCF) for 2 = 2 (1 term);
a(2): SCF for 2.7 = 2+1/(1+1/(2+1/3)) (4 terms);
a(3): SCF for 2.71 = 2+1/(1+1/(2+1/(2+1/(4+1/3)))) (6 terms).
		

Crossrefs

Cf. A080235, A080229, A011543.

Programs

Maple

Digits := 120 ;
A011543 := proc(n) floor(exp(1)*10^n) ; end proc:A179852 := proc(n) A011543(n-1)/10^(n-1) ; numtheory[cfrac](%) ; op(%) ; nops(%) ; end proc: # R. J. Mathar, Jan 14 2011