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A362447
Array A(n,k) (n>=0, k>=0) read by antidiagonals: A(n,k) = 1 if the English names for n and k have a letter in common, otherwise 0.
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1
OFFSET
0
COMMENTS
Inspired by a problem in the GCHQ Puzzle Book.
REFERENCES
GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See Problem 22, page 129.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 0..11324 (150 antidiagonals)
EXAMPLE
The top left corner of the array is:
1,1,1,1,1,1,0,1,1,1,1,...
1,1,1,1,1,1,0,1,1,1,1,...
1,1,1,1,1,0,0,0,1,0,1,...
1,1,1,1,1,1,0,1,1,1,1,...
1,1,1,1,1,1,0,0,0,0,0,...
1,1,0,1,1,1,1,1,1,1,1,...
0,0,0,0,0,1,1,1,1,1,0,...
1,1,0,1,0,1,1,1,1,1,1,...
1,1,1,1,0,1,1,1,1,1,1,...
1,1,0,1,0,1,1,1,1,1,1,...
1,1,1,1,0,1,0,1,1,1,1,...
...
The initial antidiagonals are:
1,
1,1,
1,1,1,
1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,1,
0,1,1,1,1,1,0,
1,0,0,1,1,0,0,1,
1,1,0,1,1,1,0,1,1,
1,1,0,0,1,1,0,0,1,1,
...
MATHEMATICA
iName[n_]:=iName[n]=StringDelete[IntegerName[n, "Words"], Except[LetterCharacter]];
A362447list[dmax_]:=Table[Boole[StringContainsQ[iName[n-k], Characters[iName[k]]]], {n, 0, dmax-1}, {k, 0, n}];
A362447list[20] (* Generates 20 antidiagonals *) (* Paolo Xausa, Oct 17 2023 *)
PROG
(Python)
from num2words import num2words as n2w
def w(n): return [c for c in n2w(n).replace(" and", "") if c.isalpha()]
def A(n, k): return int(set(w(n)) & set(w(k)) != set())
print([A(ad-i, i) for ad in range(13) for i in range(ad+1)]) # Michael S. Branicky, Apr 23 2023
CROSSREFS
Cf. A362448.
Sequence in context: A014446 A014883 A161996 * A242718 A015918 A016056
KEYWORD
nonn,tabl,word
AUTHOR
N. J. A. Sloane, Apr 23 2023
EXTENSIONS
a(66) and beyond from Michael S. Branicky, Apr 23 2023
STATUS
approved