A285807 Square array A(m,n) = concatenation of { m, m+1, ..., m+n }, with m, n >= 1, read by falling antidiagonals.

12, 123, 23, 1234, 234, 34, 12345, 2345, 345, 45, 123456, 23456, 3456, 456, 56, 1234567, 234567, 34567, 4567, 567, 67, 12345678, 2345678, 345678, 45678, 5678, 678, 78, 123456789, 23456789, 3456789, 456789, 56789, 6789, 789, 89, 12345678910, 2345678910, 345678910, 45678910, 5678910, 678910, 78910, 8910

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..44.

Example

A(1,1) = 12, concatenation of 1 & 2.
A(1,2) = 123, concatenation of 1, 2 and 3.
A(2,1) = 23, concatenation of 2 & 3.
The table starts:
    12    123     1234      12345       123456        1234567         12345678  ...
    23    234     2345      23456       234567        2345678         23456789  ...
    34    345     3456      34567       345678        3456789        345678910  ...
    45    456     4567      45678       456789       45678910       4567891011  ...
    56    567     5678      56789      5678910      567891011      56789101112  ...
    67    678     6789     678910     67891011     6789101112     678910111213  ...
    78    789    78910    7891011    789101112    78910111213    7891011121314  ...
    89   8910   891011   89101112   8910111213   891011121314   89101112131415  ...
   910  91011  9101112  910111213  91011121314  9101112131415  910111213141516  ...
   (...)

Prog

(PARI) a(m, n)={for(i=m+1, m+n, m=m*10^#digits(i)+i); m}

Crossrefs

Cf. A285806 for the base-2 variant.

Sequence in context: A113574 A255307 A199592 * A078189 A278982 A167208

Adjacent sequences: A285804 A285805 A285806 * A285808 A285809 A285810

Keyword

nonn,base,tabl

Author

M. F. Hasler, Apr 27 2017

Status

approved