A066686 Array T(i,j) read by antidiagonals, where T(i,j) is the concatenation of i and j (1<=i, 1<=j).

11, 12, 21, 13, 22, 31, 14, 23, 32, 41, 15, 24, 33, 42, 51, 16, 25, 34, 43, 52, 61, 17, 26, 35, 44, 53, 62, 71, 18, 27, 36, 45, 54, 63, 72, 81, 19, 28, 37, 46, 55, 64, 73, 82, 91, 110, 29, 38, 47, 56, 65, 74, 83, 92, 101, 111, 210, 39, 48, 57, 66, 75, 84, 93, 102, 111

Offset

1,1

Comments

The element at T(i,j) is the {(i+j-1)(i+j-2)/2 + i}-th element read in the sequence.

Links

Table of n, a(n) for n=1..66.

Alexander Bogomolny, What is a number?

Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

Formula

T(i, j) = i*10^A055642(i) + j. - Michael S. Branicky, Nov 21 2021

Example

The array begins
11 12 13 14 15 16 17 18 19 110 ...
21 22 23 24 25 26 27 28 29 210 ...
31 32 33 34 35 36 37 38 39 310 ...
41 42 43 44 45 46 47 48 49 410 ...

Mathematica

a = {}; Do[ a = Append[a, ToExpression[ StringJoin[ ToString[k], ToString[n - k]]]], {n, 2, 13}, {k, 1, n - 1} ]; a

Prog

(Python)
def T(i, j): return int(str(i) + str(j))
def auptodiag(maxd):
    return [T(i, d+1-i) for d in range(1, maxd+1) for i in range(1, d+1)]
print(auptodiag(12)) # Michael S. Branicky, Nov 21 2021

Crossrefs

Cf. A055642, A067574, A084854.

Sequence in context: A057303 A121979 A109372 * A125887 A303446 A350672

Adjacent sequences: A066683 A066684 A066685 * A066687 A066688 A066689

Keyword

easy,nonn,tabl,base

Author

Robert G. Wilson v, Jan 11 2002

Status

approved