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Engel expansion of cos(1)/(1+cos(1)).
2

%I #15 Feb 16 2025 08:33:19

%S 3,20,22,40,68,248,7163,28663,50059,64574,638169,761733,2537764,

%T 2925739,3363073,4977902,5646039,57212854,159650555,219684539,

%U 453524713,459239955,2002180165,3234082460,14965375439,50298730245,89316768769,464076054936,520232391320

%N Engel expansion of cos(1)/(1+cos(1)).

%C Cf. A006784 for definition of Engel expansion.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Engel_expansion">Engel Expansion</a>

%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>

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

%e 0.35077679479523758155811675...

%p Digits:= 1000:

%p 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)][]):

%p engel(b, 39);

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

%K nonn,changed

%O 1,1

%A _Alois P. Heinz_, Feb 21 2013