A362443 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.

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

Offset: 1

Author

N. J. A. Sloane, Apr 22 2023

Keywords

• nonn
• word
• fini
• full

Comments

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

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

Examples

			3 is a term because the set {20, 8, 18, 5} (from t,h,r,e,e) does not contain two consecutive numbers.
But 5 is not a term, since e and f are adjacent in the alphabet.
		

References

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

Crossrefs

Cf. A073029.

Programs

Python

from num2words import num2words as n2w
def ok(n):
    w = sorted(c for c in set(n2w(n).replace(" and", "")) if c.isalpha())
    return min(ord(w[i+1])-ord(w[i]) for i in range(len(w)-1)) > 1
print([k for k in range(100) if ok(k)]) # Michael S. Branicky, Apr 22 2023

Extensions

Terms 0 and 50 inserted by Michael S. Branicky, Apr 22 2023