A362121 a(n) is the smallest nonnegative number whose British English name has the letter "e" in the n-th position.

8, 0, 1, 3, 3, 12, 13, 17, 21, 23, 23, 73, 1700, 108, 107, 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, 101123, 101173

Offset: 1

Author

N. J. A. Sloane, Apr 20 2023

Keywords

• nonn
• word

References

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

Crossrefs

See A164790, A362120, and A362122 for other versions.

Programs

Python

from num2words import num2words
from itertools import count, islice
def n2w(n):
    return "".join(c for c in num2words(n, lang='en_GB') if c.isalpha())
def A362121(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([A362121(n) for n in range(1, 31)]) # Michael S. Branicky, Apr 21 2023

Python

# faster for initial segment of sequence; uses n2w, imports above
def A362121gen(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(A362121gen(), 50))) # Michael S. Branicky, Apr 21 2023

Extensions

a(14) and beyond from Michael S. Branicky, Apr 21 2023