login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers n such that n-th digit (after decimal point) of Pi and of Euler-Mascheroni constant gamma are the same.
1

%I #11 Sep 08 2022 08:45:47

%S 7,32,33,40,42,43,67,72,126,133,135,137,140,158,166,169,170,182,186,

%T 191,199,204,245,246,248,266,274,284,297,313,321,329,330,344,352,372,

%U 382,389,407,419,429,435,442,458,463,487,492,495,501,505,506,551,555,570

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

%F Presumably a(n) ~ 10n. - _Charles R Greathouse IV_, Sep 18 2012

%e Pi = 3.1415926535..., gamma = 0.5772156649...; seventh digit of Pi and seventh digit of gamma are both 6, hence 7 is in the sequence.

%p P:=proc(i) local a,b,n; a:=convert(evalf(gamma,1000),string); b:=convert(evalf(Pi-3,1000),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);

%o (Magma) m:=600; p:=Pi(RealField(m+1)); sp:=IntegerToString(Round(10^m*(p-3))); g:=EulerGamma(RealField(m)); sg:=IntegerToString(Round(10^m*g)); [ a: a in [1..m] | sp[a] eq sg[a] ]; // _Klaus Brockhaus_, Sep 03 2009

%Y Cf. A068394, A164820.

%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