A266002 - OEIS

A266002

Positions in Pi, e, and the Golden Ratio indicate a common digit.

13, 100, 170, 396, 500, 596, 607, 694, 825, 828, 841, 941, 1283, 1292, 1385, 1595, 1706, 1743, 1906, 2021, 2061, 2154, 2258, 2303, 2360, 2368, 2508, 2547, 2558, 2711, 2725, 2792, 2833, 2858, 3037, 3052, 3281, 3310, 3430, 3498, 3519, 3592, 3652, 3710, 3868

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..10000

EXAMPLE

The 100th digit of Pi = the 100th digit of e = the 100th digit of the Golden Ratio = 7.

MATHEMATICA

Module[{nn=10000, pid, ed, grd}, pid=RealDigits[Pi, 10, nn][[1]]; ed= RealDigits[ E, 10, nn][[1]]; grd=RealDigits[GoldenRatio, 10, nn][[1]]; Flatten[ Position[ Transpose[{pid, ed, grd}], {x_, x_, x_}]]]

PROG

(Python 3.x)

from sympy import *

#pi, E, phi

pi_const = str(N(pi, 10000))

e_const = str(N(E, 10000))

phi_const = str(S.GoldenRatio.n(10000))

for x in range(10000):

if pi_const[x] == e_const[x]:

if e_const[x] == phi_const[x]:

print(x)

# Glen Gilchrist, Jan 02 2022