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, ...).

3, 268, 375, 376, 402

Offset: 1

Author

Gonzalo Martínez, May 09 2025

Keywords

• nonn
• base
• more

Comments

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.

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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