A391761 Continued fraction that converts to its own decimal expansion; the sequence becomes strictly increasing when all zero terms are removed.

0, 3, 29, 54, 78, 438, 0, 745, 5640, 41468, 70856, 456305, 0, 810004, 0, 2384373, 3438294, 0, 31206699, 76531931, 408722091, 849627628, 4360218434, 7215407476, 34641243880, 52241626833, 77511901788, 578579632807, 741443595515, 3561938472560, 30189910604585, 61327132504535, 0, 534642368558121, 813296806630117

Offset

0,2

Comments

Because this continued fraction converts to its own decimal expansion (x = 0.3295478438074556404146870856456305081000402384373...), it is called a base-10 Trott number by Allaart.

Links

Table of n, a(n) for n=0..34.

Pieter Allaart et al., On the existence of numbers with matching continued fraction and decimal expansions, arXiv:2108.03664 [math.NT], 2022.

Eric Weisstein's World of Mathematics, Trott Constants.

Crossrefs

Cf. A039662, A091694, A113307, A378147, A391759, A391760.

Sequence in context: A071150 A107189 A059761 * A391760 A391759 A210360

Adjacent sequences: A391758 A391759 A391760 * A391762 A391763 A391765

Keyword

nonn,base,cofr

Author

Jason Bard, Dec 20 2025

Extensions

a(34) corrected by Sean A. Irvine, Dec 30 2025

Status

approved