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A254061 Decimal expansion of the generalized continued fraction with terms sigma(n)/n for n>=1. 2
4, 9, 2, 2, 7, 6, 7, 6, 1, 3, 8, 3, 0, 7, 9, 9, 4, 1, 1, 6, 5, 9, 5, 7, 1, 7, 8, 6, 6, 5, 9, 3, 6, 4, 2, 1, 7, 8, 1, 4, 2, 3, 6, 1, 8, 6, 9, 2, 5, 6, 4, 9, 6, 0, 3, 2, 6, 7, 7, 6, 0, 2, 4, 3, 4, 0, 1, 4, 2, 3, 4, 1, 6, 5, 8, 6, 1, 2, 2, 3, 9, 6, 5, 6, 8, 2, 6, 0, 5, 3, 7, 2, 4, 6, 6, 8, 4, 8, 3, 8, 1, 3, 9, 0, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The values of sigma(n)/n are: 1/1, 3/2, 4/3, 7/4, 6/5, ...

This is the limit of the expression 1/(1 + 3/(2 + 4/(3 + 7/(4 + .../...)))).

LINKS

Table of n, a(n) for n=0..104.

EXAMPLE

0.4922767613830799411659571786659364217814236186925...

PROG

(PARI) value(nn=100) = {my(v = vector(nn, n, sigma(n)/n)); for (n=1, nn, val = v[n]; forstep(k=n-1, 1, -1, val = numerator(v[k])/(denominator(v[k]) + val); ); ); print1(val*1.0); }

CROSSREFS

Cf. A017665 and A017666 (numerator and denominator of sigma(n)/n).

Cf. A254059, A254060.

Sequence in context: A006830 A238592 A229553 * A098174 A126709 A254159

Adjacent sequences: A254058 A254059 A254060 * A254062 A254063 A254064

KEYWORD

nonn,cons

AUTHOR

Michel Marcus, Jan 24 2015

STATUS

approved

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Last modified December 7 08:24 EST 2022. Contains 358649 sequences. (Running on oeis4.)