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.

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

Adjacent sequences: A362444 A362445 A362446 * A362448 A362449 A362450

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