A347765 - OEIS

%I #28 Jul 16 2022 01:08:00

%S 1,1,11,10,11,101,110,100,111,1001,1100,1010,1100,1001,11101,10000,

%T 11000,10110,11000,10001,111001,100100,110000,101000,110010,100100,

%U 111001,1000001,1100000,1011100,1100000,1000000,1110010,1001000,1100101,10100001,11000000,10010000,11100100

%N a(n) is the concatenation of terms in the n-th row of triangle A237048.

%C The number of ones in a(n) equals A001227(n).

%C The number of zeros in a(n) equals A238005(n).

%C The number of digits in a(n) equals A003056(n).

%C Therefore A238005(n) = A003056(n) - A001227(n).

%C For further information see theorem A in A238005.

%C For a nice bitmap see A347266.

%H Michael De Vlieger, <a href="/A347765/b347765.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[FromDigits@ Map[If[OddQ[#], Boole[Mod[n, #] == 0], Boole[Mod[n - #/2, #] == 0]] &, Range@ Floor[(Sqrt[8 n + 1] - 1)/2]], {n, 39}] (* _Michael De Vlieger_, Sep 15 2021 *)

%o (PARI) t(n, k) = if (k % 2, (n % k) == 0, ((n - k/2) % k) == 0);

%o a(n) = fromdigits(vector(floor((sqrt(1+8*n)-1)/2), k, t(n, k)), 10); \\ _Michel Marcus_, Sep 12 2021

%Y Cf. A003056, A007088, A001227, A196020, A237048, A237593, A238005, A347266 (decimal value).

%K nonn,base

%O 1,3

%A _Omar E. Pol_, Sep 12 2021