A355328 Decimal expansion of the number whose binary expansion differs from its decimal expansion only in the first digit.

1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1

Offset

0,1

Comments

The decimal fraction 0.1 has binary expansion starting with 0.0001...; copying the suffix 001 (3 digits, as 3 < log_2(10) < 4) we obtain 0.1001, which expands to 0.00011001101, etc.

Alternatively the process can be described as greedily expressing 1/2 with digits of weights 1/2^n-1/10^n. With f(n)=1/2^n-1/10^n, 0.5 = f(1)+f(4)+f(5)+f(8)+f(9)+f(11)...

Links

Table of n, a(n) for n=0..104.

Example

0.100110011010000011001111010001110100101001000111010001001101001011...

Mathematica

seq[len_] := Module[{s = Table[0, {len}], x = 1/10, n = 1, c = 0}, s[[1]] = 1; While[n < len, While[1/2^n - 1/10^n > x, n++]; c++; s[[n]] = 1; x -= (1/2^n - 1/10^n)]; s]; seq[100] (* Amiram Eldar, Jun 29 2022 *)

Crossrefs

Cf. A352677 (golden base = binary).

Sequence in context: A188083 A102560 A190669 * A285258 A068428 A078650

Adjacent sequences: A355325 A355326 A355327 * A355329 A355330 A355331

Keyword

nonn,cons

Author

Leonid Broukhis, Jun 29 2022

Status

approved