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
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).
Programs
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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