A175813 -id:A175813 - cp's OEIS frontend

A175792 a(n) = Sum_{k=1..n} (-1)^A000796(k), excess of the number of even over odd digits in the first n digits of Pi.

-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

Offset: 1

Michel Lagneau, Sep 06 2010

			a(6) = (-1)^3 + (-1)^1 + (-1)^4 + (-1)^1 + (-1)^5 + (-1)^9= -4.

cf. A000796, A030657, A196686 (negated), A175813 (indices of 0's).

Digits := 100:
A000796 := proc(n)
        floor(Pi*10^(n-1)) mod 10;
end proc:
A175792 := proc(n)
        add((-1)^A000796(k),k=1..n) ;
end proc: # R. J. Mathar, Jul 10 2012

Rest@ FoldList[ Plus, 0, (-1)^First@ RealDigits[Pi, 10, 200]]
Accumulate[Table[If[EvenQ[n],1,-1],{n,RealDigits[Pi,10,70][[1]]}]] (* Harvey P. Dale, Nov 03 2015 *)

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

Original entry on oeis.org

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

Zak Seidov, Oct 05 2011

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

			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.

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

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

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 *)

Definition amended by Georg Fischer, Dec 29 2021

A383690 Positions of digits in the decimal expansion of Pi where the cumulative sum of even digits equals the cumulative sum of odd digits (positions 1, 2, 3, ... refer to the digits 3, 1, 4, ...).

Original entry on oeis.org

3, 268, 375, 376, 402

Offset: 1

Gonzalo Martínez, May 09 2025

Sequence is likely finite and 402 is likely the last term. If each digit in the decimal expansion of Pi appears with the same frequency and since the sum of the odd digits is 25 and the sum of the even digits is 20, then the difference between the cumulative sum of the odd digits and the cumulative sum of the even digits tends to be positive.

Sequence inspired by the discussion of Michael S. Branicky, Jinyuan Wang and David A. Corneth.

			3 is in this sequence because when considering the first 3 decimal places in the decimal expansion of Pi, which are 3, 1 and 4, it is satisfied that 3 + 1 = 4.

Cf. A000796, A175813 (equal counts instead of equal sums).

p = RealDigits[Pi, 10, 10^4][[1]]; Flatten@ Position[ Accumulate[(-1)^p p], 0] (* Giovanni Resta, May 10 2025 *)

cp's OEIS Frontend

A175792 a(n) = Sum_{k=1..n} (-1)^A000796(k), excess of the number of even over odd digits in the first n digits of Pi.

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

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A383690 Positions of digits in the decimal expansion of Pi where the cumulative sum of even digits equals the cumulative sum of odd digits (positions 1, 2, 3, ... refer to the digits 3, 1, 4, ...).

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Mathematica