A225802 Position of first occurrence of n in continued fraction for Pi, or -1 if n never occurs.

3, 8, 0, 29, 39, 31, 1, 43, 129, 99, 275, 54, 27, 12, 2, 77, 646, 136, 139, 179, 213, 82, 202, 90, 790, 111, 573, 174, 242, 146, 877, 454, 530, 420, 1007, 593, 783, 3040, 720, 1871, 753, 118, 491, 428, 80, 3199, 824, 282, 3026, 464, 1436, 3383, 1546, 1863, 445, 1017

Offset

1,1

Comments

Correctly indexed version of A032523.

All positive integers <= 49003 occur in the first 15000000000 terms of the c.f. (the first that do not are 49004, 50471, 53486, 56315, 58255, ...) - Eric W. Weisstein, Jul 27 2013

Links

Eric W. Weisstein, Table of n, a(n) for n = 1..49003

Eric Weisstein's World of Mathematics, Pi Continued Fraction

Formula

a(n) = A032523(n) - 1.

Example

The continued fraction of Pi is [a_0; a_1, a_2, ...] = [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, ...], so
a(1) = 3 (1 first occurs at term a_3);
a(2) = 8 (2 first occurs at term a_8);
a(3) = 0 (3 first occurs at term a_0).

Crossrefs

Cf. A032523 (= a(n) + 1).

Cf. A001203 (continued fraction of Pi).

Sequence in context: A197417 A085995 A076482 * A156827 A330963 A327195

Adjacent sequences: A225799 A225800 A225801 * A225803 A225804 A225805

Keyword

nonn

Author

Eric W. Weisstein, Jul 27 2013

Extensions

"Escape clause" added to definition by Jianing Song, Apr 06 2019

Status

approved