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

1,1

References

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

Links

Table of n, a(n) for n=1..48.

Example

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

Prog

(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

Crossrefs

See A362120-A362122 for other versions.

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

Sequence in context: A309595 A329074 A296434 * A362121 A250219 A037448

Adjacent sequences: A164787 A164788 A164789 * A164791 A164792 A164793

Keyword

nonn,word

Author

Claudio Meller, Aug 26 2009

Extensions

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

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

Status

approved