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A266002
Positions in Pi, e, and the Golden Ratio indicate a common digit.
1
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
OFFSET
1,1
LINKS
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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Harvey P. Dale, Dec 19 2015
STATUS
approved