A164820 -id:A164820

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A164819

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..54.

FORMULA

Presumably a(n) ~ 10n. - Charles R Greathouse IV, Sep 18 2012

EXAMPLE

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

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);

PROG

(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

CROSSREFS

Cf. A068394, A164820.

KEYWORD

easy,nonn,base

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Aug 27 2009

EXTENSIONS

Edited and listed terms verified by Klaus Brockhaus, Sep 03 2009

STATUS

approved

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