A058935 Concatenation of first n binary numbers.

0, 1, 110, 11011, 11011100, 11011100101, 11011100101110, 11011100101110111, 110111001011101111000, 1101110010111011110001001, 11011100101110111100010011010, 110111001011101111000100110101011, 1101110010111011110001001101010111100

Offset

0,3

Comments

If the terms are read as decimal numbers, which of them are primes? For example, a(5) = 11011100101 = 1193*9229757 is not a prime. - N. J. A. Sloane, Feb 17 2023

Answer: a(231) is the first prime term when read as a decimal number; a(15) is the first when read as a binary number. - Michael S. Branicky, Feb 17 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 0..155

Eric Weisstein's World of Mathematics, Binary Champernowne Constant

Eric Weisstein's World of Mathematics, Smarandache Number

Index entries for sequences related to Most Wanted Primes video

Formula

a(n) = a(n-1)*10^A029837(n) + A007088(n).

Mathematica

FromDigits /@ Flatten /@ Rest[FoldList[Append, {}, IntegerDigits[Range[10], 2]]] (* Eric W. Weisstein, Nov 04 2015 *)

Prog

(Python)
from itertools import count, islice
def agen(s=""): yield from (int(s:=s+bin(n)[2:]) for n in count(0))
print(list(islice(agen(), 13))) # Michael S. Branicky, Feb 17 2023
(Python)
from functools import reduce
def A058935(n): return int(bin(reduce(lambda i, j:(i<<j.bit_length())+j, range(n+1)))[2:]) # Chai Wah Wu, Feb 26 2023

Crossrefs

Cf. A047778 for this converted to decimal, A001855 (offset) for number of digits.

Cf. A066716: binary Champernowne constant, A030302: binary digits, A030190: same with initial 0, A030303: indices of 1's, A007088.

Other bases: A117640 (4), A007908 (10).

Sequence in context: A267535 A267577 A262779 * A266975 A265320 A109241

Adjacent sequences: A058932 A058933 A058934 * A058936 A058937 A058938

Keyword

base,easy,nonn

Author

Henry Bottomley, Jan 12 2001

Status

approved