A175794 - OEIS

%I #13 Aug 27 2018 22:32:37

%S -1,-2,-3,-2,-3,-4,-3,-2,-1,-2,-1,-2,-3,-4,-3,-2,-1,0,1,2,3,2,1,2,3,2,

%T 3,4,5,6,7,8,9,10,9,8,9,10,11,10,9,8,7,6,5,4,3,2,1,2,1,0,-1,0,1,2,1,0,

%U 1,0,1,0,1,2,3,4,5,6,5,4,5,6,5,4,3,4,5,6,7,6,7,6,5,6,5,6,5,6,7,6,7,6,5,4,5

%N a(n) = Sum_{k=1..n} (-1)^A001620(k).

%H G. C. Greubel, <a href="/A175794/b175794.txt">Table of n, a(n) for n = 1..10000</a>

%e a(6) = -4 is in the sequence because -4 = (-1)^5 + (-1)^7 + (-1)^7 + (-1)^2 + (-1)^1 + (-1)^5

%p with(numtheory):T:=array(1..201): Digits:=200:nn:=10^200:a:=floor(evalf(gamma(0))*nn): n:=a:l:=length(n):n0:=n:s:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :T[m]:=u:od: for p from l to 1 by -1 do:s:=s+(-1)^T[p]: printf(`%d, `, s):od:

%t Rest@ FoldList[ Plus, 0, (-1)^First@ RealDigits[EulerGamma, 10, 200]] (* or *) Accumulate[(-1)^RealDigits[EulerGamma,10,100][[1]]] (* _Harvey P. Dale_, May 11 2014 *)

%Y A001620 is the decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.

%K sign,obsc,less,base

%O 1,2

%A _Michel Lagneau_, Sep 06 2010