number-theory / Normal numbers and digit expansions

Normality of a sum of two Stoneham constants

Yes: the sum of two Stoneham constants sharing a base is normal in that base, for every admissible pair of parameters, with overlapping occurrences counted. Not to be confused with what the same 2012 paper proves: its Theorem 3 shows a sum of two BB-NONnormal Stoneham constants is BB-nonnormal, which concerns a different base and the opposite property. The open half was normality in the common defining base bb, and that is what this settles.

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number-theorySep 10, 2026Significance 25/100Registry: lean verified

Normality of a sum of two Stoneham constants

Prior state unknown→proved

Yes: the sum of two Stoneham constants sharing a base is normal in that base, for every admissible pair of parameters, with overlapping occurrences counted. Not to be confused with what the same 2012 paper proves: its Theorem 3 shows a sum of two BB-NONnormal Stoneham constants is BB-nonnormal, which concerns a different base and the opposite property. The open half was normality in the common defining base bb, a…

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Yes: the sum of two Stoneham constants sharing a base is normal in that base, for every admissible pair of parameters, with overlapping occurrences counted. Not to be confused with what the same 2012 paper proves: its Theorem 3 shows a sum of two BB-NONnormal Stoneham constants is BB-nonnormal, which concerns a different base and the opposite property. The open half was normality in the common defining base bb, and that is what this settles.

Yes: the sum of two Stoneham constants sharing a base is normal in that base, for every admissible pair of parameters, with overlapping occurrences counted. Not to be confused with what the same 2012 paper proves: its Theorem 3 shows a sum of two BB-NONnormal Stoneham constants is BB-nonnormal, which concerns a different base and the opposite property. The open half was normality in the common defining base bb, and that is what this settles.

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