A159453 Smallest numbers containing exactly n smaller numbers when written as English number names.

0, 14, 21, 61, 414, 114, 122, 161, 162, 4414, 1114, 1122, 1223, 1161, 1162, 1263, 14162, 21114, 21132, 21233, 26666, 21161, 21162, 21263, 61273, 114261, 114263, 121233, 122334, 121161, 121162, 121261, 121263, 122364, 161273, 162374, 1114261, 1114263, 1122334

Offset

0,2

Comments

A159451(a(n)) = n and A159451(m) <> n for m < a(n).

Links

Michael S. Branicky, Table of n, a(n) for n = 0..80

Michael S. Branicky, Table of n, a(n) and the contained number words for n = 0..80

Michael S. Branicky, Python program

Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens

Example

a(0)=0->zero: A159451(0)=#{}=0;
a(1)=14->fourteen: A159451(14)=#{4}=1;
a(2)=21->twentyone: A159451(21)=#{1,20}=2;
a(3)=61->sixtyone: A159451(61)=#{1,6,60}=3;
a(4)=414->fourhundredfourteen: A159451(414)=#{4,14,400,404}=4;
a(5)=114->onehundredfourteen: A159451(114)=#{1,4,14,100,104}=5;
a(6)=122->onehundredtwentytwo: A159451(122)=#{1,2,20,22,100,120}=6;
a(7)=161->onehundredsixtyone: A159451(161)=#{1,6,60,61,100,106,160}=7;
a(8)=162->onehundredsixtytwo: A159451(162)=#{1,2,6,60,62,100,106,160}=8;
a(9)=4414->fourthousandfourhundredfourteen: A159451(4414)=#{4,14,400,404,414,4000,4004,4400,4404}=9;
a(10)=1114->onethousandonehundredfourteen: A159451(1114)=#{1,4,14,100,104,114,1000,1001,1100,1104}=10;
a(11)=1122->onethousandonehundredtwentytwo: A159451(1122)=#{1,2,20,22,100,120,122,1000,1001,1100,1120}=11;
a(12)=1223->onethousandtwohundredtwentythree: A159451(1223)=#{1,2,3,20,23,200,220,223,1000,1002,1200,1220}=12;
a(13)=1161->onethousandonehundredsixtyone: A159451(1161)=#{1,6,60,61,100,106,160,161,1000,1001,1100,1106,1160}=13;
a(14)=1162->onethousandonehundredsixtytwo: A159451(1162)=#{1,2,6,60,62,100,106,160,162,1000,1001,1100,1106,1160}=14;
a(15)=1263->onethousandtwohundredsixtythree: A159451(1263)=#{1,2,3,6,60,63,200,206,260,263,1000,1002,1200,1206,1260}=15.

Prog

(Python) # see Links for a faster version
from num2words import num2words
from itertools import count, islice
def n2w(n):
    map = {ord(c): None for c in "-, "}
    return num2words(n).replace(" and", "").translate(map)
def agen(): # generator of terms
    W, adict, n = set(), dict(), 0
    for m in count(0):
        w = n2w(m)
        v = len(set(w[i:j] for i in range(len(w)) for j in range(i+1, len(w)+1) if w[i:j] in W))
        if v not in adict: adict[v] = m
        while n in adict: yield adict[n]; n += 1
        W.add(w)
print(list(islice(agen(), 24))) # Michael S. Branicky, Feb 13 2024

Crossrefs

Cf. A000027, A159451, A159452.

Sequence in context: A128705 A073250 A335760 * A266651 A351689 A166628

Adjacent sequences: A159450 A159451 A159452 * A159454 A159455 A159456

Keyword

nonn,word

Author

Reinhard Zumkeller, Apr 12 2009

Extensions

a(16) and beyond from Michael S. Branicky, Feb 13 2024

Status

approved