A317422 a(n) is the smallest positive integer such that with the letters of the name of that number we can spell the name of exactly n smaller positive integers.

15, 13, 14, 21, 24, 72, 76, 74, 113, 115, 121, 171, 122, 150, 131, 142, 127, 147, 124, 129, 159, 138, 135, 153, 137, 156, 126, 125, 128, 165, 168, 157, 158, 467, 289, 265, 267, 487, 275, 392, 278, 754, 692, 492, 257, 857, 572, 524, 674, 428, 1133, 748, 1322, 867

Offset

1,1

Comments

a(2065) > 100000. - Hans Havermann, Aug 10 2018

References

Sequence Fans Mailing list.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..2064 from Hans Havermann, terms 1..100 from Daniel Suteu)

Example

a(1) = 15 because with the letters of 'fifteen' we can write only one smaller number: ten. And 15 is the smallest number for which this is so. (We cannot write 'nine' because that requires two letters 'n'.)
a(10) = 115 because with the letters of 'one hundred fifteen' we can write the name of ten smaller numbers: one, three, four, nine, ten, fourteen, fifteen, nineteen, one hundred, one hundred ten.

Prog

(Python)
from num2words import num2words as n2w
from collections import Counter
from itertools import count, islice
def key(n):
    return Counter(c for c in n2w(n).replace(" and", "") if c.isalpha())
def included(c1, c2): # in Python 3.10+, use c[i] <= c[k] in agen()
    return all(c1[c] <= c2[c] for c in c1)
def agen():
    n, adict, c = 1, {0: 1}, [None]
    for k in count(1):
        c.append(key(k))
        v = sum(1 for i in range(1, k) if included(c[i], c[k]))
        if v not in adict: adict[v] = k
        while n in adict: yield adict[n]; n += 1
        if k%10000 == 0:
            print("...", k)
print(list(islice(agen(), 54))) # Michael S. Branicky, Aug 19 2022

Crossrefs

Cf. A317423 (Spanish).

Sequence in context: A195533 A299315 A072348 * A129786 A104056 A131285

Adjacent sequences: A317419 A317420 A317421 * A317423 A317424 A317425

Keyword

nonn,word

Author

Claudio Meller, Jul 27 2018

Status

approved