A164790 a(n) is the smallest nonnegative number whose American English name has the letter "e" in the n-th position.

8, 0, 1, 3, 3, 12, 13, 17, 21, 23, 23, 73, 101, 103, 103, 112, 113, 117, 121, 123, 123, 173, 323, 373, 1103, 1103, 1112, 1113, 1117, 1121, 1123, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323, 103373, 111373

Offset: 1

Author

Claudio Meller, Aug 26 2009

Keywords

• nonn
• word

Examples

			a(1)=8 ("Eight"), a(2)=0 ("zEro"), a(3)=1 ("onE"), a(4)=3 ("thrEe").
		

References

• GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 70.

Crossrefs

See A362120-A362122 for other versions.

Cf. A164789 ("o"), A164791 ("n"), A164792 ("t"), A164793 ("i"), A164794 ("f"), A164795 ("h"), A164796 ("r"), A164797 ("u").

Programs

Python

from num2words import num2words
from itertools import count, islice
def n2w(n):
    return "".join(c for c in num2words(n).replace(" and ", "") if c.isalpha())
def A164790(n, t="e", i0=0): # t is target letter, i0 is start
    return next(i for i in count(i0) if len(w:=n2w(i))>=n and w[n-1]==t)
print([A164790(n) for n in range(1, 38)]) # Michael S. Branicky, Apr 21 2023

Python

# faster for initial segment of sequence; uses n2w/imports above
def A164790gen(t="e", i0=0, offset=1): # generator of terms w
    adict, n = dict(), offset
    for i in count(i0):
        w = n2w(i)
        if t in w:
            locs = [i+1 for i, c in enumerate(w) if w[i] == t]
            for v in locs:
                if v not in adict: adict[v] = i
        while n in adict: yield adict[n]; n += 1
print(list(islice(A164790gen(), 50))) # Michael S. Branicky, Apr 21 2023

Extensions

a(25) and beyond from Michael S. Branicky, Mar 25 2021

Name edited by N. J. A. Sloane, Apr 20 2023