mini challenge: find the smallest cosine of an integer

[Albert Chan]

Limiting x to integer ≈ (2k+1)*(pi/2)

pi/2 ≈ x / (2k+1)

Pick pi/2 convergents with odd denominator, then numerator = x

c:\> spigot -d22 -C pi/2
1/1
2/1
3/2
11/7
344/219
355/226
51819/32989
52174/33215
260515/165849
573204/364913
4846147/3085153
5419351/3450066
37362253/23785549
42781604/27235615
122925461/78256779
411557987/262005952
534483448/340262731
2549491779/1623056876
3083975227/1963319607
17969367914/11439654911
21053343141/13402974518
881156436695/560961610149
902209779836/574364584667

HP50g:
902209779836 COS       → -5.28216132855E-13 (red part should be 3683)