A052055 Positions in both Pi and e indicate a common digit.
13, 17, 18, 21, 34, 40, 45, 56, 59, 70, 81, 95, 100, 143, 170, 206, 244, 263, 275, 279, 294, 324, 326, 331, 334, 361, 365, 388, 389, 396, 412, 420, 428, 429, 453, 460, 461, 462, 484, 494, 500, 501, 504, 507, 512, 523, 526, 548, 582, 591, 595, 596, 599, 603
Offset: 1
Examples
Pi = 3.1415926535897932384626... ..................|...||..|..... _e = 2.7182818284590452353602...
Links
- Jens Kruse Andersen, Table of n, a(n) for n = 1..10000
Programs
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Maple
N:= 1000: # to get all terms <= N+1 Fpi:= convert(floor(10^N*Pi),base,10): Fe:= convert(floor(10^N*exp(1)),base,10): select(t -> Fpi[N+2-t] = Fe[N+2-t],[$2..N+1]); # Robert Israel, Jul 23 2014
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Mathematica
ed=RealDigits[N[E,2000]][[1]]; pd=RealDigits[N[\[Pi],2000]][[1]]; okQ[n_] := Take[ed,{n}] == Take[pd,{n}]; Select[Range[2000], okQ] (* Harvey P. Dale, Jan 05 2011 *) Module[{nn=3000,pid,ed},pid=RealDigits[Pi,10,nn][[1]];ed=RealDigits[ E,10,nn] [[1]]; Flatten[ Position[Transpose[{pid,ed}],{x_,x_}]]] (* Harvey P. Dale, Dec 19 2015 *) -
PARI
\p 1000 e=Vec(Str(exp(1))); p=Vec(Str(Pi)); for(n=3, #e-9, if(e[n]==p[n], print1(n-1", "))) \\ Jens Kruse Andersen, Jul 23 2014
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Python
from sympy import E, S digits = 1000 pi, e = str(S.Pi.n(digits+3)), str(E.n(digits+3)) print([k for k in range(2, digits+1) if pi[k] == e[k]]) # Michael S. Branicky, Apr 29 2023
Extensions
More terms from James Sellers, Dec 28 1999