A175792 -id:A175792 - cp's OEIS frontend

A175813 Numbers m such that the first m decimal digits of Pi contain equal numbers of even and odd decimal digits.

84, 576, 578, 580, 582, 646, 654, 682, 684, 686, 688, 690, 692, 694, 696, 698, 700, 702, 706, 722, 736, 740, 742, 2406, 2408, 2414, 2416, 2430, 2432, 2438, 2440, 2502, 2504, 2506, 2512, 2514, 2516, 2518, 2522, 2524, 2540, 2542, 2546, 2548, 2756, 2758, 2762

Offset: 1

Michel Lagneau, Sep 09 2010

Is this sequence infinite?

			84 is in the sequence because the first 84 digits of Pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986 include 42 odd digits and 42 even digits.

Pontus von Brömssen, Table of n, a(n) for n = 1..16886 (all terms below 10^9; terms 1..459 from Harvey P. Dale)

Cf. A175792.

L= Rest@FoldList[ Plus, 0, (-1)^First@ RealDigits[Pi, 10, 3000]] ;Do[If [L[[n]]==0,Print[n]],{n,3000}]
Position[Accumulate[If[EvenQ[#],1,-1]&/@(RealDigits[Pi,10,3000][[1]])],0]//Flatten (* Harvey P. Dale, Jan 10 2024 *)

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

cp's OEIS Frontend

A175813 Numbers m such that the first m decimal digits of Pi contain equal numbers of even and odd decimal digits.

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