A019440 -id:A019440 - cp's OEIS frontend

A004740 Integers in alphabetical order in U.S. English.

8, 8000000000, 8000000008, 8000000018, 8000000080, 8000000088, 8000000085

Offset: 1

Jasper Mulder, Jan 25 2010, comments that this sequence is ill-defined, since there are an infinite number of cardinal numbers that start with a 'd', namely all those powers of 10 named decillion, duodecillion and so on (see http://en.wikipedia.org/wiki/English_numerals).

However, it would seem then that 'billion' and 'centillion' also precede these, while it is standard (and systematic for this sequence) to refer to such numbers as 'one billion', 'one decillion', etc. - Yasiru Ratnayake, May 03 2012

			The list begins "eight", "eight billion", "eight billion eight", ... [corrected by _Paul Duckett_, Nov 26 2023]

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.

Cf. A019440, A026081. See A108067 for another version.

Cf. A073327, A152611, A075831, A000052.

A026081 Integers in reverse alphabetical order in U.S. English.

Original entry on oeis.org

0, 2202202202202, 2202202202222, 2202202202223, 2202202202226

Offset: 1

Neil Fernandez

This sequence is ill-defined from the 2nd term on. Proof: Assume that x is the term following the initial 0. Then the number x*10^(6n), for n sufficiently large, is spelled out: name(x) name(10^(6n)). This comes after name(x) in lexicographical order, and thus before x in this sequence. - M. F. Hasler, Nov 20 2009

			Zero, two trillion, two hundred and two billion, two hundred and two million, two hundred and two thousand, two hundred and two, ...

Cf. A004740, A019440.

See A127352 for another version. - N. J. A. Sloane, Dec 05 2009

A127352 Integers less than 10^303 in reverse alphabetical order in U.S. English.

Original entry on oeis.org

0, 2000000000000000000000000002000000000000000000000002000000002202, 2000000000000000000000000002000000000000000000000002000000002222, 2000000000000000000000000002000000000000000000000002000000002223, 2000000000000000000000000002000000000000000000000002000000002226, 2000000000000000000000000002000000000000000000000002000000002227, 2000000000000000000000000002000000000000000000000002000000002221

Offset: 1

Michael B. Porter, Nov 24 2009

Since the use of alphabetic names is rare for numbers greater than 10^15, there is no universal agreement on the naming scheme for large integers, and there is some question whether this sequence would well-defined without the "less than 10^303" clause.
The Wikipedia article compares 8 dictionary sources and has names for the powers of 1000 up to 10^63 and for 10^303. These are also in the Mathworld link.
There are several conflicting schemes for extending the dictionary definitions. If we assume that the system of alphabetic names greater than 10^63 defines a word for every power of 1000 and that word comes before "vigintillion" alphabetically, the sequence can include all integers. However, many of the extension schemes listed do not meet that standard - some have multiple words and some have words that are alphabetically after "vigintillion".
For the powers of 1000 between 10^66 and 10^303, one source (http://www.mrob.com/pub/math/largenum.html) coins the name "vigintinonillion" for 10^90, but this format is inconsistent with other names listed in the same source, e.g. "duovigintillion", "sexoctogintillion". The name "novemvigintillion" seems to be more common. Otherwise, all sources have "vigintillion" as alphabetically last of all the powers of 1000 up to 10^303.
The terms are from Andrew Weimholt.

			zero,
two vigintillion two undecillion two trillion two thousand two hundred two,
two vigintillion two undecillion two trillion two thousand two hundred twenty two, etc.

Michael B. Porter, Table of n, a(n) for n = 1..15
Robert P. Munafo, Large numbers
Landon Curt Noll, How high can you count?
John J. G. Savard, Some notes on big numbers
Gerard Schildberger, Lists of Words for the Numbers in A060365 and A060366
Eric Weisstein's World of Mathematics, Large Number
Wikipedia, Names of large numbers

Cf. A004740, A019440, A060365, A060366.

See A026081 for another version.

A119796 Zero through ten in alphabetical order of English reverse spelling.

Original entry on oeis.org

3, 9, 1, 5, 10, 7, 0, 2, 4, 8, 6

Offset: 1

Jonathan Vos Post, Jul 30 2006

			a(1) = 3 because EERHT comes alphabetically first.
a(2) = 9 because ENIN comes alphabetically second.
a(3) = 1 because ENO comes alphabetically third.
a(4) = 5 because EVIF comes alphabetically fourth.

Cf. A000052, A004740, A019440, A026081, A001058, A057846, A108067, A072991.

A119898 1-digit numbers arranged in alphabetical order of English spelling reversed, then the 2-digit numbers so arranged, then the 3-digit numbers, etc.

Original entry on oeis.org

3, 9, 1, 5, 7, 0, 2, 4, 8, 6, 93, 53, 83, 73, 23, 33, 43, 63, 99, 59, 89, 79, 29, 39, 49, 69, 91, 51, 81, 71, 21, 31, 41, 61, 95, 55, 85, 75, 25, 35, 45, 65, 12, 19, 15, 18, 17, 13, 14, 16, 10, 11, 97, 57, 87, 77, 27, 37, 47, 67, 92, 52, 82, 72, 22, 32, 42, 62, 94, 54, 84, 74, 24

Offset: 1

Jonathan Vos Post, Aug 01 2006

Analog of A000052 where the alphabetical order is applied not to English name of integer but to the English name whose letters are then reversed.

			Eerht, Enin, Eno, Evif, Neves, Orez, Owt, Ruof, Thgie, Xis;
Eerhtytenin, Eerhtytfif, Eerhtythgie, Eerhtytneves, Eerhtytnewt, Eerhtytriht, Eerhtytrof, Eerhtytxis, Eninytenin, Eninytfif, Eninythgie, Eninytneves, Eninytnewt, Eninytriht, Eninytrof, Eninytxis, Enoytenin, Enoytfif, Enoythgie, Enoytneves, Enoytnewt, Enoytriht, Enoytrof, Enoytxis, Evifytenin, Evifytfif, ...

Cf. A000052, A004740, A019440, A026081, A001058, A057846, A108067, A072991.

f[a_, b_] := Sort@ Table[{ StringReverse[ StringReplace[ IntegerName[h, "Words"], {"\[Hyphen]" -> ""}]], h}, {h, a, b}]; Last /@ Join[f[0, 9], f[10, 99]] (* Giovanni Resta, Jun 13 2016 *)

Data and example corrected by Giovanni Resta, Jun 13 2016

A290483 Integers in alphabetical order in Spanish, using the long scale.

Original entry on oeis.org

14, 14000000000000, 14000000000014, 14000000014000, 14000000014014, 14000000014100, 14000000014114, 14000000014105, 14000000014150, 14000000014155, 14000000014154, 14000000014152, 14000000014159, 14000000014158, 14000000014156, 14000000014157, 14000000014153, 14000000014151, 14000000014140, 14000000014145

Offset: 1

Jose M. Arenas, Aug 03 2017

This sequence uses the long scale of numbers, so 10^9 is Thousand Millions (Mil Millones) and not One Billion (Un Billón).

			14 = "catorce".
14000000000000 = "catorce billones".
14000000000014 = "catorce billones catorce".
14000000014000 = "catorce billones catorce mil".
14000000014014 = "catorce billones catorce mil catorce".
14000000014100 = "catorce billones catorce mil cien".
14000000014114 = "catorce billones catorce mil ciento catorce".
14000000014105 = "catorce billones catorce mil ciento cinco".
14000000014150 = "catorce billones catorce mil ciento cincuenta".
14000000014155 = "catorce billones catorce mil ciento cincuenta y cinco".
14000000014154 = "catorce billones catorce mil ciento cincuenta y cuatro".
14000000014152 = "catorce billones catorce mil ciento cincuenta y dos".
14000000014159 = "catorce billones catorce mil ciento cincuenta y nueve".
14000000014158 = "catorce billones catorce mil ciento cincuenta y ocho".
14000000014156 = "catorce billones catorce mil ciento cincuenta y seis".
14000000014157 = "catorce billones catorce mil ciento cincuenta y siete".
14000000014153 = "catorce billones catorce mil ciento cincuenta y tres".
14000000014151 = "catorce billones catorce mil ciento cincuenta y uno".
14000000014140 = "catorce billones catorce mil ciento cuarenta".
14000000014145 = "catorce billones catorce mil ciento cuarenta y cinco".

Jose M. Arenas, Table of n, a(n) for n = 1..10000

Cf. A004740, A019440, A097960, A108067, A126686, A161390.

cp's OEIS Frontend

A004740 Integers in alphabetical order in U.S. English.

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A026081 Integers in reverse alphabetical order in U.S. English.

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A127352 Integers less than 10^303 in reverse alphabetical order in U.S. English.

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A119796 Zero through ten in alphabetical order of English reverse spelling.

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A119898 1-digit numbers arranged in alphabetical order of English spelling reversed, then the 2-digit numbers so arranged, then the 3-digit numbers, etc.

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A290483 Integers in alphabetical order in Spanish, using the long scale.

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