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

0,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A102931 A056447 A056437 * A012275 A067608 A023177

Adjacent sequences: A309317 A309318 A309319 * A309321 A309322 A309323

Keyword

nonn,base,easy

Author

James Carruthers, Sep 21 2019

Status

approved