A222481 -id:A222481 - cp's OEIS frontend

A222480 Decimal expansion of cos(1)/(1+cos(1)).

3, 5, 0, 7, 7, 6, 7, 9, 4, 7, 9, 5, 2, 3, 7, 5, 8, 1, 5, 5, 8, 1, 1, 6, 7, 5, 0, 5, 7, 2, 8, 2, 0, 1, 7, 1, 1, 0, 3, 8, 5, 7, 2, 3, 8, 9, 2, 2, 5, 4, 9, 7, 9, 7, 6, 4, 3, 9, 9, 4, 8, 4, 2, 1, 4, 8, 4, 7, 2, 6, 5, 0, 7, 8, 7, 0, 9, 7, 9, 0, 9, 0, 8, 9, 3, 4, 4, 0, 1, 1, 0, 7, 4, 1, 8, 8, 7, 3, 1, 1, 5, 0, 8, 1, 2, 7, 9, 2, 4, 2, 2, 5, 0, 1, 4, 1, 6, 3, 2, 8, 6, 2

Offset: 0

Alois P. Heinz, Feb 21 2013

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 13 2019

			0.35077679479523758155811675...

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

Cf. A222481 (continued fraction), A222482 (Engel expansion), A049470 (cos(1)), A073448 (1/cos(1)).

s:= convert(evalf(1/(1+1/cos(1)), 140), string):
seq(parse(s[n+2]), n=0..122);

1/(1+1/cos(1)) \\ Charles R Greathouse IV, May 13 2019

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

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

A222480 Decimal expansion of cos(1)/(1+cos(1)).

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