A309320 a(n) is the smallest positive integer m such that the digits of n in base 10 are also the first digits of sin(m) in base 10 after the decimal point.

0, 3, 6, 53, 9, 10, 7, 4, 1, 2, 91, 69, 47, 25, 3, 41, 63, 85, 107, 129, 151, 160, 138, 116, 94, 72, 50, 6, 16, 38, 60, 82, 104, 148, 170, 163, 141, 97, 75, 53, 31, 9, 13, 57, 79, 101, 145, 167, 166, 122, 100, 78, 34, 12, 10, 32, 76, 98, 120, 164, 147, 125, 81

Offset: 0

Author

James Carruthers, Sep 21 2019

Keywords

• nonn
• base
• easy

Examples

			a(1) = 3 because we have sin(1.) = 0.8414709848..., sin(2.) = 0.9092974268..., sin(3.) = 0.1411200081.. - _N. J. A. Sloane_, Sep 28 2019
		

Links

• James Carruthers, Table of n, a(n) for n = 0..10000

Programs

Mathematica

a[0] =0; a[n_] := Module[{m = 1}, While[(d = IntegerDigits[n]) != RealDigits[ Sin[m], 10, Length[d], -1][[1]], m++]; m]; Array[a, 100, 0] (* Amiram Eldar, Sep 28 2019 *)

Python

import numpy as np
import math as m
n = 1
i = 0
inp = np.zeros(1)
out = inp
while n < 10001:
    k=m.fabs( m.trunc( m.sin(i) * m.pow( 10,m.floor( m.log10(n)+1 ) ) ) )
    if k==n:
        inp = np.append(inp,int(n))
        out = np.append(out,int(i))
        print(n,i)
        n += 1
        i = 0
        continue
    else:
        i+=1