A378147 The lexicographically earliest infinite simple continued fraction such that the concatenation of its terms has the same succession of digits as its decimal expansion.

0, 3, 29, 5, 710, 9, 8, 9, 2, 10, 6, 7, 2, 3, 8, 6, 8, 5, 3, 3, 2, 3, 5, 1, 5, 9, 4, 8, 8, 2, 50, 4, 8, 2, 5, 2, 7, 20, 3, 1, 5, 4, 8, 5, 5, 7, 9, 9, 1, 90, 2, 8, 8, 3, 6, 5, 5, 2, 50, 3, 9, 5, 4, 1, 80, 3, 1, 9, 3, 5, 8, 7, 1, 1, 7, 7, 8, 5, 9, 2, 4, 2, 5, 4

Offset

0,2

Comments

In the first 10000 terms, the only values with more than a single nonzero digit are a(2) = 29 and a(4) = 710.

Links

Dominic McCarty, Table of n, a(n) for n = 0..10000

Dominic McCarty, Java program for A378147

Example

0 + 1/(3 + 1/(29 + 1/(5 + 1/(710 + 1/(9 + 1/(8 + 1/(9 + 1/(2 + 1/(10 + ...)))))))))
= [0; 3, 29, 5, 710, 9, 8, 9, 2, 10, ...]
= 0.3295710989210...

Crossrefs

Sequence in context: A096621 A362466 A143234 * A071195 A292625 A030274

Adjacent sequences: A378144 A378145 A378146 * A378148 A378149 A378150

Keyword

base,cofr,nonn

Author

Dominic McCarty, Jan 07 2025

Status

approved