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

Author

Paolo P. Lava and Giorgio Balzarotti, Aug 27 2009

Keywords

• easy
• nonn
• base

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.
		

Crossrefs

Cf. A068394, A164820.

Programs

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

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