A222480 -id:A222480 - cp's OEIS frontend

A222481 Continued fraction for cos(1)/(1+cos(1)).

0, 2, 1, 5, 1, 2, 2, 1, 2, 1, 1, 40, 4, 3, 1, 3, 4, 46, 3, 5, 2, 12, 3, 1, 4, 11, 1, 3, 3, 106, 2, 1, 1, 2, 28, 1, 7, 32, 3, 42, 1, 9, 1, 4, 2, 2, 1, 1, 15, 1, 5, 1, 8, 1, 1, 1, 3, 1, 7, 18, 13, 1, 1, 1, 1, 1, 5, 9, 7, 3, 3, 1, 1, 18, 6, 5, 1, 11, 1, 1, 10, 2

Offset: 0

Alois P. Heinz, Feb 21 2013

Essentially the same as A068115: a(n) = A068115(n) for n != 2.

			0.35077679479523758155811675...

Cf. A222480 (decimal expansion), A222482 (Engel expansion), A049470 (cos(1)), A073448 (1/cos(1)), A068115.

numtheory[cfrac](evalf(1/(1+1/cos(1)), 250), 130, 'quotients')[];

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

Offset changed by Andrew Howroyd, Jul 03 2024

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

Original entry on oeis.org

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

Alois P. Heinz, Feb 21 2013

nonn

Cf. A006784 for definition of Engel expansion.

			0.35077679479523758155811675...

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

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

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);

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

cp's OEIS Frontend

A222481 Continued fraction for cos(1)/(1+cos(1)).

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