A164820 Numbers n such that n-th digit (after decimal point) of e and of Euler-Mascheroni constant gamma are the same.
4, 30, 33, 34, 48, 49, 52, 59, 60, 66, 96, 113, 115, 134, 146, 155, 163, 169, 175, 180, 193, 196, 200, 206, 211, 235, 251, 274, 288, 300, 302, 304, 330, 336, 338, 350, 354, 358, 368, 373, 381, 399, 412, 419, 430, 436, 438, 440, 491, 506, 536, 542, 552, 579
Offset: 1
Examples
e = 2.7182818284..., gamma = 0.5772156649...; fourth digit of e and fourth digit of gamma are both 2, hence 4 is in the sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Magma
m:=600; e:=Exp(One(RealField(m+1))); se:=IntegerToString(Round(10^m*(e-2))); g:=EulerGamma(RealField(m)); sg:=IntegerToString(Round(10^m*g)); [ a: a in [1..m] | se[a] eq sg[a] ]; // Klaus Brockhaus, Sep 03 2009
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Maple
P:=proc(i) local a,b,c,d,n; a:=convert(evalf(gamma,1000),string); b:=convert(evalf(exp(1)-2,1000),string); for n from 2 by 1 to i do if substring(a,n)=substring(b,n) then print(n-1); fi; od; end: P(900);
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Mathematica
With[{nn=600},Position[Thread[{Rest[RealDigits[E,10,nn+1][[1]]], RealDigits[ EulerGamma,10,nn][[1]]}],{x_,x_}]]//Flatten (* Harvey P. Dale, Oct 08 2017 *)
Extensions
Edited and listed terms verified by Klaus Brockhaus, Sep 03 2009