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

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

Crossrefs

Cf. A000796, A001113, A001622, A257492, A257494.

Sequence in context: A155646 A089936 A196928 * A367554 A326864 A083341

Adjacent sequences: A265999 A266000 A266001 * A266003 A266004 A266005

Keyword

nonn,base

Author

Harvey P. Dale, Dec 19 2015

Status

approved