cp's OEIS Frontend

A058935 Concatenation of first n binary numbers.

%I A058935 #40 Feb 16 2025 08:32:43
%S A058935 0,1,110,11011,11011100,11011100101,11011100101110,11011100101110111,
%T A058935 110111001011101111000,1101110010111011110001001,
%U A058935 11011100101110111100010011010,110111001011101111000100110101011,1101110010111011110001001101010111100
%N A058935 Concatenation of first n binary numbers.
%C A058935 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
%C A058935 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
%H A058935 Michael S. Branicky, <a href="/A058935/b058935.txt">Table of n, a(n) for n = 0..155</a>
%H A058935 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinaryChampernowneConstant.html">Binary Champernowne Constant</a>
%H A058935 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheNumber.html">Smarandache Number</a>
%H A058935 <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>
%F A058935 a(n) = a(n-1)*10^A029837(n) + A007088(n).
%t A058935 FromDigits /@ Flatten /@ Rest[FoldList[Append, {}, IntegerDigits[Range[10], 2]]] (* _Eric W. Weisstein_, Nov 04 2015 *)
%o A058935 (Python)
%o A058935 from itertools import count, islice
%o A058935 def agen(s=""): yield from (int(s:=s+bin(n)[2:]) for n in count(0))
%o A058935 print(list(islice(agen(), 13))) # _Michael S. Branicky_, Feb 17 2023
%o A058935 (Python)
%o A058935 from functools import reduce
%o A058935 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
%Y A058935 Cf. A047778 for this converted to decimal, A001855 (offset) for number of digits.
%Y A058935 Cf. A066716: binary Champernowne constant, A030302: binary digits, A030190: same with initial 0, A030303: indices of 1's, A007088.
%Y A058935 Other bases: A117640 (4), A007908 (10).
%K A058935 base,easy,nonn
%O A058935 0,3
%A A058935 _Henry Bottomley_, Jan 12 2001