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Decimal expansion of the number whose base-3 expansion is A004601, the base-2 expansion of Pi.

0

`%I #10 Jul 19 2024 19:13:14
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`%S 4,0,3,8,4,1,7,2,3,8,6,2,7,1,2,0,1,0,3,4,2,3,6,4,9,2,2,5,9,2,9,2,1,8,
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`%T 6,6,7,4,5,3,1,5,7,8,4,0,1,3,9,5,3,3,5,5,3,4,2,3,3,7,0,1,9,3,5,9,4,5,
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`%U 0,1,6,0,8,1,0,4,7,9,0,7,6,2,8,5,4,8,8,8,0,7,5,9,9,8,8,8
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`%N Decimal expansion of the number whose base-3 expansion is A004601, the base-2 expansion of Pi.
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`%C This number is likely to be normal in base 2 but certainly not normal in base 3, where it has only digits 0 and 1.
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`%H Wikipedia, <a href="https://en.m.wikipedia.org/wiki/Normal_number">Normal number</a>, retrieved July 17, 2024
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`%F 4.03841723862712010342364922592921866745315784013953355342337019359450160810479...
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`%e Pi = 3.14159...[10] = 11.001001000011111101...[2] (i.e., in base 2, cf. A004601), which, considered as the base-3 expansion of a constant c = 3 + 1 + 1/3^3 + 1/3^6 + ... = 4.0384...[10]
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`%o (PARI) localprec(10+ N=99); d = concat(binary(Pi)); c = sum(k=1, #d, d[k]*3^(2-k),.); digits(c*10^N\1) /* if you use localprec() make sure all code is in the same scope */
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`%Y Cf. A000796 (decimal expansion of Pi), A004601 (binary expansion of Pi).
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`%K nonn,base,cons
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`%O 1,1
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`%A _M. F. Hasler_, Jul 17 2024
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