A196686 Number of odd digits of Pi minus number of even digits.

1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 5, 6, 7, 8, 7, 8, 7, 6, 5, 4, 3, 2, 3, 4, 3, 4, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 12, 11, 10, 9, 10, 11, 10, 11, 10, 9, 10, 11, 10, 11, 10, 11, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 2, 1, 0, -1, -2, -1, -2, -3, -4, -3, -2, -3, -4, -3, -2

Offset: 1

Author

Zak Seidov, Oct 05 2011

Keywords

• sign
• base

Comments

Cumulative sum of A030657 with zeros replaced by "-1".

Examples

			Among first 10 digits of Pi, {3,1,4,1,5,9,2,6,5,3}, there are 7 odd and 3 even, hence a(10)=7-3=4.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000 [a(10000) corrected by _Georg Fischer_, Dec 29 2021]
• Zak Seidov, Dependence a(n) for n = 1..10000
• Zak Seidov, Dependence a(n) for n = 1..10^6

Crossrefs

Cf. A030657, A175792 (negated), A175813 (indices of 0's).

Programs

Mathematica

rd=RealDigits[N[Pi, 10004]][[1]]; a=0; s=Reap[Do[a=a+2Mod[rd[[n]],2]-1; Sow[{n,a}], {n,10004}]][[2,1]] (* this gives b-file *) (* Zak Seidov, Oct 05 2011 *)
Module[{nn=100,pid},pid=RealDigits[Pi,10,nn][[1]];Accumulate[If[OddQ[#],1,-1]&/@pid]] (* Harvey P. Dale, Feb 23 2025 *)

Extensions

Definition amended by Georg Fischer, Dec 29 2021