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

1,1

Links

Table of n, a(n) for n=1..54.

Mathematica

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

Prog

(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

Crossrefs

Cf. A052055, A257494.

Sequence in context: A166534 A126727 A340618 * A067912 A140646 A109656

Adjacent sequences: A257489 A257490 A257491 * A257493 A257494 A257495

Keyword

nonn,base

Author

Harvey P. Dale, Apr 26 2015

Status

approved