%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