A285806 Square array A(m,n) = number whose binary expansion is the concatenation of those of { m, m+1, ..., m+n }, with m, n >= 1, read by falling antidiagonals.

6, 27, 11, 220, 92, 28, 1765, 741, 229, 37, 14126, 5934, 1838, 302, 46, 113015, 47479, 14711, 2423, 375, 55, 1808248, 759672, 235384, 38776, 6008, 888, 120, 28931977, 12154761, 3766153, 620425, 96137, 14217, 1929, 137, 462911642, 194476186, 60258458, 9926810, 1538202, 227482, 30874, 2202, 154

Offset

1,1

Comments

A column n = 0 would have A(m,0) = m. A row m = 0 would have A(0,n) = A(1,n-1) for all n > 0.

Links

Table of n, a(n) for n=1..45.

Example

A(1,1) = 6 = 110[2], concatenation of 1 & 2 written in binary.
A(1,2) = 27 = 110101[2], concatenation of 1 & 2 & 3 written in binary.
A(2,1) = 11 = 1011[2], concatenation of 2 & 3 written in binary.
The table starts:
     6   27   220   1765    14126    113015    1808248     28931977     462911642
    11   92   741   5934    47479    759672   12154761    194476186    3111618987
    28  229  1838  14711   235384   3766153   60258458    964135339   15426165436
    37  302  2423  38776   620425   9926810  158828971   2541263548   40660216781
    46  375  6008  96137  1538202  24611243  393779900   6300478413  100807654622
    55  888 14217 227482  3639723  58235580  931769293  14908308702  238532939247
   120 1929 30874 493995  7903932 126462925 2023406814  32374509039 1035984289264
   137 2202 35243 563900  9022413 144358622 2309737967  73911614960 2365171678737
   154 2475 39612 633805 10140894 162254319 5192138224 166148423185 5316749541938

Prog

(PARI) a(m, n)={for(i=m+1, m+n, m=m<<#binary(i)+i); m}

Crossrefs

Cf. A285807 for the base-10 variant.

Sequence in context: A137088 A356813 A179162 * A292384 A183603 A067876

Adjacent sequences: A285803 A285804 A285805 * A285807 A285808 A285809

Keyword

nonn,base,tabl

Author

M. F. Hasler, Apr 27 2017

Status

approved