A222482 Engel expansion of cos(1)/(1+cos(1)).

3, 20, 22, 40, 68, 248, 7163, 28663, 50059, 64574, 638169, 761733, 2537764, 2925739, 3363073, 4977902, 5646039, 57212854, 159650555, 219684539, 453524713, 459239955, 2002180165, 3234082460, 14965375439, 50298730245, 89316768769, 464076054936, 520232391320

Offset: 1

Author

Alois P. Heinz, Feb 21 2013

Keywords

• nonn

Comments

Cf. A006784 for definition of Engel expansion.

Examples

			0.35077679479523758155811675...
		

Links

• Eric Weisstein's World of Mathematics, Engel Expansion
• Wikipedia, Engel Expansion
• Index entries for sequences related to Engel expansions

Crossrefs

Cf. A222480 (decimal expansion), A222481 (continued fraction), A049470 (cos(1)), A073448 (1/cos(1)).

Programs

Maple

Digits:= 1000:
b:= evalf(1/(1+1/cos(1))):  engel:= (r, n)-> `if`(n=0 or r=0, NULL, [ceil(1/r), engel(r*ceil(1/r)-1, n-1)][]):
engel(b, 39);

Formula

cos(1)/(1+cos(1)) = 1/(1+1/cos(1)) = 1/(1+sec(1)).