%I #11 Apr 23 2023 07:27:51

%S 0,2,3,4,6,7,9,10,11,19,20,23,29,40,42,50,52,90,99

%N Numbers k with property that the set of letters in the English name for k does not contain two letters that are adjacent in the alphabet.

%C In other words, k such that row k of the triangle A073029, when converted to a set, does not contain two consecutive numbers.

%C Since hundred, thousand, million, all contain two consecutive letters, there are no other terms.

%D GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See pages 99 and 286.

%e 3 is a term because the set {20, 8, 18, 5} (from t,h,r,e,e) does not contain two consecutive numbers.

%e But 5 is not a term, since e and f are adjacent in the alphabet.

%o (Python)

%o from num2words import num2words as n2w

%o def ok(n):

%o w = sorted(c for c in set(n2w(n).replace(" and", "")) if c.isalpha())

%o return min(ord(w[i+1])-ord(w[i]) for i in range(len(w)-1)) > 1

%o print([k for k in range(100) if ok(k)]) # _Michael S. Branicky_, Apr 22 2023

%Y Cf. A073029.

%K nonn,word,fini,full

%O 1,2

%A _N. J. A. Sloane_, Apr 22 2023

%E Terms 0 and 50 inserted by _Michael S. Branicky_, Apr 22 2023