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A257492
Positions where Pi and the Golden Ratio have a common decimal digit.
3
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
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
Sequence in context: A166534 A126727 A340618 * A067912 A140646 A109656
KEYWORD
nonn,base
AUTHOR
Harvey P. Dale, Apr 26 2015
STATUS
approved