A237129 Let d = d(1)d(2)... d(q) denote the decimal expansion of an angle d expressed in degrees. The sequence a(n) lists the angles such that sin(d) = cos(d(1)*d(2)*... *d(q)).

90, 418, 450, 666, 726, 778, 786, 810, 1146, 1170, 1386, 1395, 1530, 1775, 1890, 2218, 2250, 2394, 2474, 2482, 2610, 2842, 2898, 2970, 3186, 3195, 3312, 3330, 3366, 3375, 3690, 3711, 3735, 3915, 3933, 3978, 4050, 4146, 4194, 4274, 4282, 4338, 4410, 4698, 4770

Offset: 1

Author

Michel Lagneau, Feb 04 2014

Keywords

• nonn
• base

Examples

			666 is in the sequence because sin(666°) = cos(6*6*6°) = -.8090169943749... = -phi/2 where phi is the golden ratio (1+sqrt(5))/2. (A019863)
418 is in the sequence because sin(418°) = cos(4*1*8°)= .84804809615... (A019867)
3915 is in the sequence because sin(3915°) = cos(3*9*1*5°)= -.70710678118654752440 = -1/sqrt(2). (A010503)
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..2000

Programs

Maple

with(numtheory):err:=1/10^10:Digits:=20:for n from 1 to 5000 do:x:=convert(n,base,10):n1:=nops(x):p:=product('x[i]', 'i'=1..n1):s1:=evalf(sin(n*Pi/180)):s2:=evalf(cos(p*Pi/180)):if abs(s1-s2)