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A066686
Array T(i,j) read by antidiagonals, where T(i,j) is the concatenation of i and j (1<=i, 1<=j).
9
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
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
KEYWORD
easy,nonn,tabl,base
AUTHOR
Robert G. Wilson v, Jan 11 2002
STATUS
approved