A000052 -id:A000052 - cp's OEIS frontend

A109986 Primes ordered alphabetically by where they occur in A000052.

5, 7, 3, 2, 89, 83, 11, 59, 53, 41, 47, 43, 19, 97, 17, 79, 71, 73, 61, 67, 13, 31, 37, 29, 23, 881, 887, 883, 811, 859, 857, 853, 809, 877, 863, 839, 829, 821, 827, 823, 587, 557, 541, 547, 509, 599, 593, 571, 577, 569, 563, 503, 521, 523, 487, 457, 449, 443

Offset: 1

Jonathan Vos Post, Jul 07 2005

A109987 is semiprimes ordered alphabetically by where they occur in A000052. A109988 is 3-almost primes ordered alphabetically by where they occur in A000052.

			a(1) = 5 because five is the first prime in alphabetical order.
a(5) = 89 because eighty-nine is the first 2-digit prime in alphabetical order.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000040, A000052, A109987, A109988.

V:= [seq(select(isprime, [$10^i..10^(i+1)-1]),i=0..3)]:
seq(op(V[i][sort(map(convert,V[i],english,'And'),
output=permutation)]),i=1..nops(V)); # Robert Israel, Jun 17 2016

alph = Last /@ Import["https://oeis.org/A000052/b000052.txt", "Table"]; Take[
Select[alph, PrimeQ], 58] (* Giovanni Resta, Jun 17 2016 *)

Corrected and extended by Giovanni Resta, Jun 17 2016

A109987 Semiprimes ordered alphabetically by where they occur in A000052.

Original entry on oeis.org

4, 9, 6, 85, 87, 86, 82, 15, 58, 55, 51, 57, 49, 46, 14, 95, 94, 91, 93, 74, 77

Offset: 1

Jonathan Vos Post, Jul 07 2005

A109986 is primes ordered alphabetically by where they occur in A000052. A109988 is 3-almost primes ordered alphabetically by where they occur in A000052.

			a(1) = 4 because four is the first semiprime in alphabetical order.
a(4) = 85 because eighty-five is the first 2-digit semiprime in alphabetical order.

Cf. A000052, A001358, A109986, A109988.

A109988 3-almost primes (A014612) ordered alphabetically by where they occur in A000052.

Original entry on oeis.org

8, 18, 50, 52, 45, 44, 42, 98, 99, 92, 70, 78, 75, 76

Offset: 1

Jonathan Vos Post, Jul 07 2005

A109986 is primes ordered alphabetically by where they occur in A000052. A109987 is semiprimes ordered alphabetically by where they occur in A000052. A109989 is 4-almost primes ordered alphabetically by where they occur in A000052.

			a(1) = 8 because eight is the first 3-almost prime in alphabetical order.
a(4) = 18 because eighteen is the first 2-digit 3-almost prime in alphabetical order.

Cf. A000052, A014612, A109986, A109987.

A109989 4-almost primes (A014613) ordered alphabetically by where they occur in A000052.

Original entry on oeis.org

88, 84, 81, 54, 56, 40, 90

Offset: 1

Jonathan Vos Post, Jul 07 2005

A109986 is primes ordered alphabetically by where they occur in A000052. A109987 is semiprimes ordered alphabetically by where they occur in A000052. A109988 is 3-almost primes ordered alphabetically by where they occur in A000052.

			a(1) = 88 because eighty-eight is the first 4-almost prime in alphabetical order, there being no 1-digit 4-almost primes.
a(2) = 84 because eighty-four is the second 2-digit 4-almost prime in alphabetical order.

Cf. A000052, A014613, A109986, A109987, A109988.

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

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Neil Fernandez

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.

A158352 a(n) is the smallest number whose name in US English contains n vowels.

Original entry on oeis.org

2, 1, 11, 14, 71, 101, 111, 114, 171, 1071, 1101, 1111, 1114, 1171, 11171, 14171, 71171, 101171, 111171, 114171, 171171, 1071171, 1101171, 1111171, 1114171, 1171171, 11171171, 14171171, 71171171, 101171171, 111171171, 114171171, 171171171, 1071171171, 1101171171

Offset: 1

Rodolfo Kurchan, Mar 16 2009

In US English, "101" is written as "one hundred one".
From Michael S. Branicky, Oct 24 2020 (Start)
The sequence counts vowels by counting the instances of the letters 'a', 'e', 'i', 'o', 'u', and 'y' (see Example). If 'y' were not included, then a(5) = 102 ("OnE hUndrEd twO") is the first among subsequent value changes.
In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used. Also, the common written form is adopted ("one thousand one hundred seventeen" not "eleven hundred seventeen"; Wilson link).
Also, a(n) = A158353(n) for n >= 3. Proof. For them to differ after (171)^n, which has 9*n vowels, would require either (i) "one [power name] two" be next, preceding "one [power name] one"), which could only occur if [power name] had 9*n-2 vowels; or (ii) [power name] has > 9*n-2 vowels and a subsequent power name has less (within a range depending on n). Neither case occurs for existing names (see Wikipedia Large numbers link). (End)

			"twO" has 1 vowel, "OnE" has 2, "ElEvEn" has 3, "fOUrtEEn" has 4, "sEvEntY-OnE" has 5, "OnE hUndrEd OnE" has 6, "OnE hUndrEd ElEvEn" has 7.

Eric Weisstein's World of Mathematics, Large Number
Wikipedia, Names of Large Numbers
Wiktionary, one hundred one (US)
Wiktionary, one hundred and one (UK)
Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens

Cf. A000052, A079741, A158353.

With[{s = Array[StringCount[StringJoin@ Map[If[IntegerQ[#], IntegerName[#], ToString[#]] &, ToExpression@ StringSplit@ IntegerName[#]], {"a", "e", "i", "o", "u", "y"}] &, 10^4]}, Array[FirstPosition[s, #][[1]] &, Max@ s]] (* Michael De Vlieger, Nov 06 2020 *)

from num2words import num2words
def A158352(n):
  i = 1
  while sum(1 for c in num2words(i).replace(' and ', '') if c in "aeiouy")!=n:
    i += 1
  return i
print([A158352(n) for n in range(1,16)]) # Michael S. Branicky, Oct 23 2020

Edited by Jon E. Schoenfield, Sep 29 2018

a(9) onwards from Michael S. Branicky, Oct 23 2020

A001058 1-digit numbers in reverse alphabetical order, then 2-digit numbers, etc.

Original entry on oeis.org

0, 2, 3, 6, 7, 1, 9, 4, 5, 8, 22, 23, 26, 27, 21, 29, 24, 25, 28, 20, 12, 32, 33, 36, 37, 31, 39, 34, 35, 38, 30, 13, 10, 62, 63, 66, 67, 61, 69, 64, 65, 68, 60, 16, 72, 73, 76, 77, 71, 79, 74, 75, 78, 70, 17, 92, 93, 96, 97, 91, 99, 94, 95, 98, 90, 19, 14, 42, 43, 46, 47, 41

Offset: 1

N. J. A. Sloane, Vijay10(AT)aol.com (Ajay Sudan)

This uses the standard US English names for numbers. - Daniel Forgues, May 11 2016

Ben Hamilton, Brainteasers and Mindbenders, Fireside, 1992, p. 19.

Cf. A000052.

A158353 a(n) is the smallest number greater than a(n-1) whose name in US English contains n vowels.

Original entry on oeis.org

2, 3, 11, 14, 71, 101, 111, 114, 171, 1071, 1101, 1111, 1114, 1171, 11171, 14171, 71171, 101171, 111171, 114171, 171171, 1071171, 1101171, 1111171, 1114171, 1171171, 11171171, 14171171, 71171171, 101171171, 111171171, 114171171, 171171171, 1071171171, 1101171171

Offset: 1

Rodolfo Kurchan, Mar 16 2009

In US English, "101" is written as "one hundred one".
From Michael S. Branicky, Oct 24 2020 (Start)
The sequence counts vowels by counting the instances of the letters 'a', 'e', 'i', 'o', 'u', and 'y' (see Example). If 'y' were not included, then a(5) = 102 ("OnE hUndrEd twO") is the first among subsequent value changes.
In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used. Also, the common written form is adopted ("one thousand one hundred seventeen" not "eleven hundred seventeen"; Wilson link).
Also, a(n) = A158352(n) for n >= 3. (proof in A158352).
(End)

			"twO" has 1 vowel, "thrEE" has 2, "ElEvEn" has 3, "fOUrtEEn" has 4, "sEvEntY-OnE" has 5, "OnE hUndrEd OnE" has 6, "OnE hUndrEd ElEvEn" has 7.

Eric Weisstein's World of Mathematics, Large Number
Wikipedia, Names of Large Numbers
Wiktionary, one hundred one (US)
Wiktionary, one hundred and one (UK)
Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens

Cf. A000052, A079741, A158352.

from num2words import num2words
def A158353upto(n):
  i, ans = 1, []
  for k in range(1, n+1):
    while sum(1 for c in num2words(i).replace(' and ', '') if c in "aeiouy") != k:
      i += 1
      ans.append(i)
  return ans
print(A158353upto(20)) # Michael S. Branicky, Oct 23 2020

Edited by Jon E. Schoenfield, Sep 29 2018

a(9) and beyond from Michael S. Branicky, Oct 23 2020

A072991 Numbers 1 through 10 in alphabetical order.

Original entry on oeis.org

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

Offset: 1

Brian Nichols (brni(AT)weinberggroup.com), Aug 21 2002

A000052 is a better version of this sequence.

A097960 Arrange 1-digit numbers in Spanish in alphabetical order, then 2-digit numbers, then 3-digit numbers, etc.

Original entry on oeis.org

0, 5, 4, 2, 9, 8, 6, 7, 3, 1, 14, 50, 55, 54, 52, 59, 58, 56, 57, 53, 51, 40, 45, 44, 42, 49, 48, 46, 47, 43, 41, 19, 18, 16, 17, 10, 12, 90, 95, 94, 92, 99, 98, 96, 97, 93, 91, 80, 85, 84, 82, 89, 88, 86, 87, 83, 81, 11, 15, 60, 65, 64, 62, 69, 68, 66, 67, 63, 61, 70, 75, 74, 72

Offset: 1

Colin Backhurst (colin.backhurst(AT)ntlworld.com), Sep 21 2004

In the 2007 Spanish film "Fermat's Room", a mathematician solves the "enigma" of how the numbers 5, 4, 2, 9, 8, 6, 7, 3, 1 are ordered. - Jonathan Sondow, Jul 20 2012

			0="cero", 5="cinco", 4="cuatro", 2="dos", 9="nueve", 8="ocho", 6="seis", 7="siete", 3="tres", 1="un".

Álvar Ibeas, Table of n, a(n) for n = 1..10001
Wikipedia, Fermat's Room

Cf. A000052 (English).

cp's OEIS Frontend

A109986 Primes ordered alphabetically by where they occur in A000052.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A109987 Semiprimes ordered alphabetically by where they occur in A000052.

Views

Author

Keywords

Comments

Examples

Crossrefs

A109988 3-almost primes (A014612) ordered alphabetically by where they occur in A000052.

Views

Author

Keywords

Comments

Examples

Crossrefs

A109989 4-almost primes (A014613) ordered alphabetically by where they occur in A000052.

Views

Author

Keywords

Comments

Examples

Crossrefs

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

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

A158352 a(n) is the smallest number whose name in US English contains n vowels.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A001058 1-digit numbers in reverse alphabetical order, then 2-digit numbers, etc.

Views

Author

Keywords

Comments

References

Crossrefs

A158353 a(n) is the smallest number greater than a(n-1) whose name in US English contains n vowels.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Extensions

A072991 Numbers 1 through 10 in alphabetical order.

Views

Author

Keywords

Crossrefs

A097960 Arrange 1-digit numbers in Spanish in alphabetical order, then 2-digit numbers, then 3-digit numbers, etc.

Views