A119523: Decimal expansion of the van der Waerden–Ulam binary measure of the primes.
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The formula is , where is the characteristic function of the primes. The primes have a larger measure than the composites because they dominate the smaller integers.
The binary expansion of the van der Waerden–Ulam binary measure of the primes being obviously (see A010051)
0.1101010001010001010001000001010000010001010001... |
The quaternary (base 4) expansion of the van der Waerden–Ulam binary measure of the primes being (see A??????)
0.31101101101001100101101... |
In the quaternary expansion all the digits after the point, with the exception of the initial 3, are 0 or 1 since there is only one even prime.
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