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

Author

Robert G. Wilson v, Jan 11 2002

Keywords

• easy
• nonn
• tabl
• base

Comments

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

Examples

			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 ...
		

Links

• Alexander Bogomolny, What is a number?
• Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Cf. A055642, A067574, A084854.

Programs

Mathematica

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

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

Formula

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