%I #13 Sep 08 2022 08:45:47

%S 4,30,33,34,48,49,52,59,60,66,96,113,115,134,146,155,163,169,175,180,

%T 193,196,200,206,211,235,251,274,288,300,302,304,330,336,338,350,354,

%U 358,368,373,381,399,412,419,430,436,438,440,491,506,536,542,552,579

%N Numbers n such that n-th digit (after decimal point) of e and of Euler-Mascheroni constant gamma are the same.

%H Harvey P. Dale, <a href="/A164820/b164820.txt">Table of n, a(n) for n = 1..1000</a>

%e e = 2.7182818284..., gamma = 0.5772156649...; fourth digit of e and fourth digit of gamma are both 2, hence 4 is in the sequence.

%p 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);

%t 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 *)

%o (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

%Y Cf. A068394, A164819.

%K easy,nonn,base

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Aug 27 2009

%E Edited and listed terms verified by _Klaus Brockhaus_, Sep 03 2009