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A058935
Concatenation of first n binary numbers.
12
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
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
KEYWORD
base,easy,nonn
AUTHOR
Henry Bottomley, Jan 12 2001
STATUS
approved