A164819 Numbers n such that n-th digit (after decimal point) of Pi and of Euler-Mascheroni constant gamma are the same.
7, 32, 33, 40, 42, 43, 67, 72, 126, 133, 135, 137, 140, 158, 166, 169, 170, 182, 186, 191, 199, 204, 245, 246, 248, 266, 274, 284, 297, 313, 321, 329, 330, 344, 352, 372, 382, 389, 407, 419, 429, 435, 442, 458, 463, 487, 492, 495, 501, 505, 506, 551, 555, 570
Offset: 1
Examples
Pi = 3.1415926535..., gamma = 0.5772156649...; seventh digit of Pi and seventh digit of gamma are both 6, hence 7 is in the sequence.
Programs
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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
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Maple
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);
Formula
Presumably a(n) ~ 10n. - Charles R Greathouse IV, Sep 18 2012
Extensions
Edited and listed terms verified by Klaus Brockhaus, Sep 03 2009