A053977 Engel expansion of the Euler-Mascheroni constant gamma A001620 = 0.57721566... .

2, 7, 13, 19, 85, 2601, 9602, 46268, 4812284, 147961485, 210810243, 814960948, 1003849128, 1016803038, 12917183059, 26242325020, 22215291139324, 30797877759859, 60139200644343, 121848657453426, 133555928335475

Offset

1,1

Comments

Cf. A006784 for definition of Engel expansion.

References

F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.

Links

T. D. Noe, Table of n, a(n) for n=1..300

F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.

P. Erdős and Jeffrey Shallit, New bounds on the length of finite Pierce and Engel series, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.

Eric Weisstein's World of Mathematics, Engel Expansion

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant

Index entries for sequences related to Engel expansions

Mathematica

EngelExp[ A_, n_ ] := Join[ Array[ 1&, Floor[ A ] ], First@Transpose@NestList[ {Ceiling[ 1/Expand[ #[ [ 1 ] ]#[ [ 2 ] ]-1 ] ], Expand[ #[ [ 1 ] ]#[ [ 2 ] ]-1 ]}&, {Ceiling[ 1/(A-Floor[ A ]) ], A-Floor[ A ]}, n-1 ] ]

Crossrefs

Cf. A006784, A028254, A028257.

Sequence in context: A237499 A231476 A138042 * A079381 A079382 A111354

Adjacent sequences: A053974 A053975 A053976 * A053978 A053979 A053980

Keyword

nonn,easy,nice

Author

Jeppe Stig Nielsen, Apr 02 2000

Extensions

More terms and additional comments from Mitch Harris, Jan 15 2001

Status

approved