A257492 Positions where Pi and the Golden Ratio have a common decimal digit.

13, 15, 19, 43, 46, 49, 53, 60, 64, 66, 71, 78, 100, 102, 107, 108, 114, 134, 138, 139, 140, 158, 162, 170, 171, 173, 177, 178, 185, 191, 196, 230, 240, 254, 271, 290, 304, 314, 322, 360, 368, 395, 396, 402, 407, 416, 437, 439, 440, 443, 448, 465, 468, 472

Offset: 1

Author

Harvey P. Dale, Apr 26 2015

Keywords

• nonn
• base

Crossrefs

Cf. A052055, A257494.

Programs

Mathematica

With[{nn=1000},Flatten[Position[Thread[{RealDigits[GoldenRatio,10,nn][[1]],RealDigits[Pi,10,nn][[1]]}],_?(#[[1]]==#[[2]]&),{1},Heads-> False]]]

Python

from sympy import S
digits = 1000
pi, phi = str(S.Pi.n(digits+3)), str(S.GoldenRatio.n(digits+3))
print([k for k in range(2, digits+1) if pi[k] == phi[k]]) # Michael S. Branicky, May 06 2023