A373462 Decimal expansion of the number whose base-3 expansion is A004601, the base-2 expansion of Pi.

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, 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, 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

Offset: 1

Author

M. F. Hasler, Jul 17 2024

Keywords

• nonn
• base
• cons

Comments

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.

Examples

			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]
		

Links

• Wikipedia, Normal number, retrieved July 17, 2024

Crossrefs

Cf. A000796 (decimal expansion of Pi), A004601 (binary expansion of Pi).

Programs

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 */

Formula

4.03841723862712010342364922592921866745315784013953355342337019359450160810479...