A164797 -id:A164797

A164790

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

+10
13

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

(list; graph; refs; listen; history; text; internal format)

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").

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

A164791

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

+10
9

9, 1, 9, 20, 7, 11, 15, 13, 17, 47, 27, 77, 109, 120, 107, 111, 115, 113, 117, 147, 127, 177, 327, 377, 1120, 1107, 1111, 1115, 1113, 1117, 1147, 1127, 1177, 1327, 1377, 3327, 3377, 11377, 13327, 13377, 17377, 23327, 23377, 73377, 101377, 103327, 103377

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

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

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

a(1)=9 ("Nine"), a(2)=1 ("oNe"), a(3)=9 ("niNe"), a(4)=20 ("tweNty").

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 a(n):

return next(i for i in count(0) if len(w:=n2w(i))>=n and w[n-1]=="n")

print([a(n) for n in range(1, 41)]) # Michael S. Branicky, Apr 21 2023

(Python) # faster for initial segment of sequence; uses n2w, imports above

def agen(): # generator of terms

adict, n = dict(), 1

for i in count(0):

w = n2w(i)

if "n" in w:

locs = [i+1 for i, c in enumerate(w) if w[i] == "n"]

for v in locs:

if v not in adict: adict[v] = i

while n in adict: yield adict[n]; n += 1

print(list(islice(agen(), 50))) # Michael S. Branicky, Apr 21 2023

CROSSREFS

Cf. A164789 ("o"), A164790 ("e"), A164792 ("t"), A164793 ("i"), A164794 ("f"), A164795 ("h"), A164796 ("r"), A164797 ("u").

KEYWORD

nonn,word

AUTHOR

Claudio Meller, Aug 26 2009

EXTENSIONS

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

Definition clarified by N. J. A. Sloane, Apr 20 2023. We also need a British English analog of this, just as A362121 is an analog of A164790 (a(13) will be different).

STATUS

approved

A164789

a(n) is the smallest number which has in its English name the letter "o" in the n-th position, or -1 if no such number exists.

+10
8

1, 4, 2, 0, 4000000000000000000000000000, 41, 21, 24, 22, 72, 101, 104, 102, 304, 302, 141, 121, 124, 122, 172, 322, 372, 1104, 1102, 1304, 1302, 1141, 1121, 1124, 1122, 1172, 1322, 1372, 3322, 3372, 11372, 13322, 13372, 17372, 23322, 23372, 73372, 101372, 103322, 103372

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

a(1)=1 ("One"), a(2)=4 ("fOur"), a(3)=2 ("twO"), a(4)=0 ("zerO"), a(5)=4*10^27 ("fourOctillion").

CROSSREFS

Cf. A164790 ("e"), A164791 ("n"), A164792 ("t"), A164793 ("i").

Cf. A164794 ("f"), A164795 ("h"), A164796 ("r"), A164797 ("u").

KEYWORD

word,sign

AUTHOR

Claudio Meller, Aug 26 2009

EXTENSIONS

a(5) corrected and a(23) and beyond from Michael S. Branicky, Mar 25 2021

STATUS

approved

A164792

a(n) is the smallest number whose English name has the letter "t" in the n-th position, or -1 if no such number exists.

+10
8

2, -1, -1, 15, 8, 17, 22, 72, 13000, 48, 28, 78, 302, 115, 108, 117, 122, 172, 322, 148, 128, 178, 328, 378, 1115, 1108, 1117, 1122, 1172, 1322, 1148, 1128, 1178, 1328, 1378, 3328, 3378, 11378, 13328, 13378, 17378, 23328, 23378, 73378, 101378, 103328, 103378

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

a(1)=2 ("Two"), a(4)=15 ("fifTeen"), a(9)=13000 ("thirteenThousand"), a(13)=302 ("threehundredTwo").

CROSSREFS

Cf. A164789 ("o"), A164790 ("e"), A164791 ("n"), A164793 ("i").

Cf. A164794 ("f"), A164795 ("h"), A164796 ("r"), A164797 ("u").

KEYWORD

word,sign

AUTHOR

Claudio Meller, Aug 26 2009

EXTENSIONS

a(9) corrected, and a(25) and beyond from Michael S. Branicky, Feb 02 2021

STATUS

approved

A164793

a(n) is the smallest number whose English name has the letter "i" in the n-th position, or -1 if no such number exists.

+10
8

-1, 5, 13, -1, 1000000, 4000000, 45, 25, 75, 13000000, 17000000, 105, 113, 305, 313, 3013, 145, 125, 175, 325, 375, 3075, 1105, 1113, 1305, 1313, 3305, 1145, 1125, 1175, 1325, 1375, 3325, 3375, 11375, 13325, 13375, 17375, 23325, 23375, 73375, 101375, 103325

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Original definition used "-2 for infinite".

LINKS

Table of n, a(n) for n=1..43.

EXAMPLE

a(2)=5 ("fIve"), a(3)=13 ("thIrteen"), a(5)=10^6 ("onemIllion").

CROSSREFS

Cf. A164789 ("o"), A164790 ("e"), A164791 ("n"), A164792 ("t").

Cf. A164794 ("f"), A164795 ("h"), A164796 ("r"), A164797 ("u").

KEYWORD

word,sign

AUTHOR

Claudio Meller, Aug 26 2009

EXTENSIONS

a(11) and beyond from Michael S. Branicky, Feb 02 2021

Name changed to remove "-2" (see Comments), and a(1) and a(4) changed from -2 to -1 by Jon E. Schoenfield, Feb 02 2021

STATUS

approved

A164794

a(n) is the smallest number whose English name has the letter "f" in the n-th position, or -1 if no such number exists.

+10
8

4, -1, 15, -1, -1, 44, 24, 74, -1, -1, 104, 404, 115, 415, 315, 144, 124, 174, 324, 374, 3074, 1104, 1404, 1115, 1415, 1315, 1144, 1124, 1174, 1324, 1374, 3324, 3374, 11374, 13324, 13374, 17374, 23324, 23374, 73374, 101374, 103324, 103374, 111374, 113324

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

a(1)=4 ("Four"), a(3)=15 ("fiFteen"), a(11)=104 ("onehundredFour").

CROSSREFS

Cf. A164789 ("o"), A164790 ("e"), A164791 ("n"), A164792 ("t").

Cf. A164793 ("i"), A164795 ("h"), A164796 ("r"), A164797 ("u").

KEYWORD

word,sign

AUTHOR

Claudio Meller, Aug 26 2009

EXTENSIONS

a(21) and beyond from Michael S. Branicky, Feb 02 2021

STATUS

approved

A164795

a(n) is the smallest number whose English name has the letter "h" in the n-th position, or -1 if no such number exists.

+10
8

-1, 3, -1, 8, 400, 300, 43, 23, 48, 28, 78, 103, 403, 108, 408, 308, 143, 123, 148, 128, 178, 328, 378, 1403, 1108, 1408, 1308, 1143, 1123, 1148, 1128, 1178, 1328, 1378, 3328, 3378, 11378, 13328, 13378, 17378, 23328, 23378, 73378, 101378, 103328, 103378

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..46.

EXAMPLE

a(2)=3 ("tHree"), a(4)=8 ("eigHt"), a(12)=103 ("onehundredtHree").

CROSSREFS

Cf. A164789 ("o"), A164790 ("e"), A164791 ("n"), A164792 ("t").

Cf. A164793 ("i"), A164794 ("f"), A164796 ("r"), A164797 ("u").

KEYWORD

word,sign

AUTHOR

Claudio Meller, Aug 26 2009

EXTENSIONS

a(24) and beyond from Michael S. Branicky, Feb 02 2021

STATUS

approved

A164796

a(n) is the smallest number whose English name has the letter "r" in the n-th position, or -1 if no such number exists.

+10
8

-1, -1, 0, 4, 1000000000000, 4000000000000, 3000000000000, 43, 23, 24, 74, 24000000000000, 103, 104, 303, 304, 3004, 143, 123, 124, 174, 324, 374, 1103, 1104, 1303, 1304, 3303, 1143, 1123, 1124, 1174, 1324, 1374, 3324, 3374, 11374, 13324, 13374, 17374, 23324

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..41.

EXAMPLE

a(3)=0 ("zeRo"), a(4)=4 ("fouR"), a(5)=1000000000000 ("onetRillion"), a(13)=103 ("onehundredthRee").

CROSSREFS

Cf. A164789 ("o"), A164790 ("e"), A164791 ("n"), A164792 ("t").

Cf. A164793 ("i"), A164794 ("f"), A164795 ("h"), A164797 ("u").

KEYWORD

word,sign

AUTHOR

Claudio Meller, Aug 26 2009

EXTENSIONS

a(24) and beyond from Michael S. Branicky, Feb 02 2021

STATUS

approved