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a(n) = Sum_{k=1..n} (-1)^A001622(k).
1

%I #9 Apr 21 2021 15:39:57

%S -1,0,-1,0,1,0,-1,-2,-1,0,-1,0,-1,0,-1,0,1,2,3,4,5,6,5,6,7,8,7,8,7,8,

%T 7,8,7,8,7,6,5,4,5,6,5,6,5,4,3,2,3,4,3,2,3,4,5,6,7,6,5,4,5,6,7,8,9,10,

%U 9,10,9,10,11,12,13,14,15,16,15,16,15,16,17,18,19,18,17,18,17,18,19,18,19

%N a(n) = Sum_{k=1..n} (-1)^A001622(k).

%C A cumulative sum over the parities of the decimals in the decimal expansion of the golden ratio A001622.

%e a(7) = -1 because, with 7 digits of phi = 1.618033... we obtain:

%e (-1)^1 + (-1)^6 + (-1)^1 + (-1)^8 + (-1)^0 + (-1)^3 + (-1)^3 = -1.

%t Rest@ FoldList[ Plus, 0, (-1)^First@ RealDigits[GoldenRatio, 10, 200]]

%Y Cf. A001622.

%K sign,base,less

%O 1,8

%A _Michel Lagneau_, Sep 10 2010