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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.
+0
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
EXAMPLE
a(1)=2 ("Two"), a(4)=15 ("fifTeen"), a(9)=13000 ("thirteenThousand"), a(13)=302 ("threehundredTwo").
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.
+0
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
COMMENTS
Original definition used "-2 for infinite".
EXAMPLE
a(2)=5 ("fIve"), a(3)=13 ("thIrteen"), a(5)=10^6 ("onemIllion").
EXTENSIONS
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
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.
+0
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
EXAMPLE
a(1)=4 ("Four"), a(3)=15 ("fiFteen"), a(11)=104 ("onehundredFour").
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.
+0
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
EXAMPLE
a(2)=3 ("tHree"), a(4)=8 ("eigHt"), a(12)=103 ("onehundredtHree").
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.
+0
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
EXAMPLE
a(3)=0 ("zeRo"), a(4)=4 ("fouR"), a(5)=1000000000000 ("onetRillion"), a(13)=103 ("onehundredthRee").
a(n) is the smallest nonnegative number whose American English name has the letter "n" in the n-th position.
+0
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
REFERENCES
GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 70.
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")
(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
EXTENSIONS
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).
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.
+0
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
EXAMPLE
a(1)=1 ("One"), a(2)=4 ("fOur"), a(3)=2 ("twO"), a(4)=0 ("zerO"), a(5)=4*10^27 ("fourOctillion").
a(n) is the smallest nonnegative number whose American English name has the letter "e" in the n-th position.
+0
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
REFERENCES
GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 70.
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)
(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
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