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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 22 20:14 EDT 2024. Contains 374540 sequences. (Running on oeis4.)