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

Author

Eric W. Weisstein, Jul 27 2013

Keywords

• nonn

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

Examples

			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).
		

Links

• Eric W. Weisstein, Table of n, a(n) for n = 1..49003
• Eric Weisstein's World of Mathematics, Pi Continued Fraction

Crossrefs

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

Cf. A001203 (continued fraction of Pi).

Formula

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

Extensions

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