A347266 a(n) is the number whose binary representation is the concatenation of terms in the n-th row of A237048.

1, 1, 3, 2, 3, 5, 6, 4, 7, 9, 12, 10, 12, 9, 29, 16, 24, 22, 24, 17, 57, 36, 48, 40, 50, 36, 57, 65, 96, 92, 96, 64, 114, 72, 101, 161, 192, 144, 228, 136, 192, 178, 192, 129, 473, 288, 384, 320, 388, 304, 456, 258, 384, 353, 801, 520, 912, 576, 768, 676, 768, 576, 922, 512, 801, 1409

Offset

1,3

Comments

The number of ones in the n-th row of A237048 equals A001227(n), the same as the number of ones in the binary representation of a(n).

The number of zeros in the n-th row of A237048 equals A238005(n), the same as the number of zeros in the binary representation of a(n).

The number of terms in the n-th row of A237048 equals A003056(n), the same as the number of digits in the binary representation of a(n).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Bitmap of the first 2^10 terms, showing 1s in black, 12X horizontal exaggeration.

Michael De Vlieger, Bitmap of the first 2^12 terms, showing 1s in black, rotated 90 degrees counterclockwise. [Click "magnify" to see the graph more clearly.]

Example

The 15th row of the triangle A237048 is [1, 1, 1, 0, 1] and the concatenation of these terms is 11101 which can be interpreted as a binary number whose decimal value is 29, so a(15) = 29.

Mathematica

Table[FromDigits[Boole[Divisible[n - If[OddQ[#], 0, Quotient[#, 2]], #]] & /@ Range[Quotient[Sqrt[8 n + 1] - 1, 2]], 2], {n, 66}] (* Jan Mangaldan, Sep 13 2021 *)

Prog

(PARI) t(n, k) = if (k % 2, (n % k) == 0, ((n - k/2) % k) == 0);
a(n) = fromdigits(vector(floor((sqrt(1+8*n)-1)/2), k, t(n, k)), 2); \\ Michel Marcus, Sep 12 2021

Crossrefs

Cf. A003056, A007088, A001227, A237048, A237593, A238005, A347765 (binary representation).

Sequence in context: A023605 A223542 A182003 * A050060 A247829 A351705

Adjacent sequences: A347263 A347264 A347265 * A347267 A347268 A347269

Keyword

nonn,base,look

Author

Omar E. Pol, Sep 06 2021

Status

approved