A224847 Position of first occurrence of n in the continued fraction for the Euler-Mascheroni constant (gamma).

1, 3, 8, 7, 10, 68, 23, 13, 138, 51, 21, 160, 9, 198, 336, 78, 162, 175, 383, 613, 182, 650, 136, 479, 249, 861, 553, 617, 286, 299, 1951, 165, 149, 2037, 559, 482, 1283, 680, 305, 19, 348, 1129, 2279, 1883, 1902, 2563, 4752, 716, 30, 2609, 567, 247, 2170, 7776

Offset: 1

Author

Eric W. Weisstein, Jul 22 2013

Keywords

• nonn

Comments

This sequence is the same as A033149, but uses correct [a_0; a_1, a_2, ...] indexing of continued fraction terms.

The smallest numbers not occurring in the first 4,851,382,841 terms of the c.f. are 27943, 33436, 33978, 34017, ... - Eric W. Weisstein, Jul 22 2013

Examples

			The c.f. for gamma is  A002852 = [0; 1, 1, 2, 1, 2, 1, 4, 3, 13, ...].
1 occurs first at term a_1
2 occurs first at term a_3.
3 occurs first at term a_8.
4 occurs first at term a_7.
		

Links

• Eric W. Weisstein, Table of n, a(n) for n = 1..27942
• Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant Continued Fraction

Crossrefs

Cf. A033149(n) = a(n) + 1.

Cf. A002852 (continued fraction for Euler-Mascheroni constant).

Programs

Mathematica

With[{cfeg=Rest[ContinuedFraction[EulerGamma,8000]]},Table[Position[cfeg,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Nov 06 2024 *)