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A059093 Numbers ending with the letter "e" (in English).

1, 3, 5, 9, 12, 21, 23, 25, 29, 31, 33, 35, 39, 41, 43, 45, 49, 51, 53, 55, 59, 61, 63, 65, 69, 71, 73, 75, 79, 81, 83, 85, 89, 91, 93, 95, 99, 101, 103, 105, 109, 112, 121, 123, 125, 129, 131, 133, 135, 139, 141, 143, 145, 149, 151, 153, 155, 159, 161, 163, 165

Offset: 1

Nancy Bancroft (nbancroft(AT)home.com), Feb 12 2001

a(n+1)=a((n mod 37)+1)+100*floor(n/37) for n>=1.

More terms and formula from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001

A059437 Consider the last letter of each of the English words zero, one, two, three, four, five, ... . Write down 0 for a vowel or "y", 1 for a consonant.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1

Offset: 0

Franklin T. Adams-Watters, Apr 09 2009

A variant of A152592.

A059852 Consider the English alphabet in Morse code (the International Morse radio telegraph code). Map a 'dit' to the digit one and a 'dah' to the digit 2, then express that ternary number in decimal.

Original entry on oeis.org

5, 67, 70, 22, 1, 43, 25, 40, 4, 53, 23, 49, 8, 7, 26, 52, 77, 16, 13, 2, 14, 41, 17, 68, 71, 76

Offset: 1

Robert G. Wilson v, Feb 27 2001

Written in base 3, the terms read (12, 2111, 2121, 211, 1, 1121, 221, 1111, 11, 1222, 212, 1211, 22, 21, 222, 1221, 2212, 121, 111, 2, 112, 1112, 122, 2112, 2122, 2211). This contains all words over {1,2} with 1 to 4 letters except for 1122, 1212, 2221 and 2222, which correspond to the codes for Ü, Ä, Ö and CH. - M. F. Hasler, Jun 22 2020

			The sixth letter, F, is ".._." in Morse. This becomes 1121 in ternary and 43 in decimal, so a(6) = 43.

"Learning the Radiotelegraph Code," Seventh Edition, published by American Radio Relay League, West Hartford 7, Connecticut, 1955.
"Morse Code Course," Jeppesen and Company, Denver, Colorado, 1962.
"International Morse Code," prepared by Lt. Commander F.R.L. Tuthill, USNR and Lt. (J.G.) E.L. Battey, USNR, published by Insuline Corporation of America, Long Island City, NY.

Wikipedia, Morse code.

Cf. A060110, the same for numbers, and A060109, written in base 3.
Cf. A008777 (number of base 3 digits = dots and dashes in the n-th letter), A281015, A281017, A281018.
Cf. A105386, A105387 (ambiguous variants using digits 0 and 1).

A059852=digits(3008707498660932665486381130661318784490079420090,81) \\ or vecextract(apply(A032924,[1..28]), i) with i=numtoperm(26, 58849338891424664724588744) or i=vecsort(Vec("ETIANMSURWDKGOHVFuLaPJBXCYZQ"),,1)[1..26]. - M. F. Hasler, Jun 22 2020

Edited, links and crossrefs added by M. F. Hasler, Jun 22 2020

A104059 Each number is the rank in the alphabet of a letter (and "0" stands for a space). After substitution one reads (in English): "twenty twentythree five fourteen twenty twentyfive zero..." which is exactly the sequence itself (without hyphens).

Original entry on oeis.org

20, 23, 5, 14, 20, 25, 0, 20, 23, 5, 14, 20, 25, 20, 8, 18, 5, 5, 0, 6, 9, 22, 5, 0, 6, 15, 21, 18, 20, 5, 5, 14, 0, 20, 23, 5, 14, 20, 25, 0, 20, 23, 5, 14, 20, 25, 6, 9, 22, 5, 0, 26, 5, 18, 15, 0, 20, 23, 5, 14, 20, 25, 0, 20, 23, 5, 14, 20, 25, 20, 8, 18, 5, 5, 0, 6, 9, 22, 5, 0, 6, 15

Offset: 1

Eric Angelini, Mar 02 2005

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

nlim := 82: words := ["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen", "twenty", "twentyone", "twentytwo", "twentythree", "twentyfour", "twentyfive", "twentysix"]: A104059str := "twenty": lettonum := proc (let) if let = " " then return 0: end if: return convert(let, bytes)[1]-96: end proc: printf("20, "): for n from 2 to nlim do t := lettonum(A104059str[n]): A104059str := cat(A104059str, " ", words[t+1]): printf("%d, ", t): end do: # Nathaniel Johnston, Oct 28 2013

a(27) and a(28) corrected by J.J.J. Klein, Oct 28 2013

A119945 Sum of numerical values of letters in German names of the nonnegative numbers.

Original entry on oeis.org

59, 47, 63, 36, 54, 52, 54, 54, 32, 54, 53, 23, 87, 89, 107, 105, 88, 88, 85, 107, 106, 173, 208, 181, 199, 197, 199, 199, 177, 199, 90, 157, 192, 165, 183, 181, 183, 183, 161, 183, 96, 163, 198, 171, 189, 187, 189, 189, 167, 189, 94, 161, 196, 169, 187, 185, 187, 187, 165

Offset: 0

Wolfdieter Lang, Jul 20 2006

Letters with umlauts are interpreted respectively as "ae" (which does not appear in this entry), "oe", "ue", and "sz" (sharp s) (as in the German name of 30 = "dreißig" -> "dreissig") as "ss" (not "sz").
According to the Reder reference only "zweihundertfuenf", 205 and "zweihundertsieben", 207, satisfy a(n)=n.
This sequence is ambiguous for numbers above 100 because one can use, for instance, for 101 "hundertundeins" or "hunderteins. To avoid such ambiguities one should always stick to the shorter version.
An alternate version of this sequence could ignore umlauts (i.e., take "a" for "ä" etc), or, more in-line with the German alphabet as it is usually listed in textbooks and reference works, taken as ä=27, ö=28, ü=29 (and then maybe ß=30, which could nonetheless remain considered as a ligature of "∫s"="ss"). - M. F. Hasler, Jun 23 2013
It appears that there is no canonical version of this sequence, because of the lack of agreement even on the number of letters in the German alphabet. - N. J. A. Sloane, Jun 11 2021

			"Null" for 0 in German has numerical values (a=1, b=2, ..., z=26) [14, 21, 12, 12] which sums up to a(0)=59.
The numerical values for "zweihundertfuenf" are [26, 23, 5, 9, 8, 21, 14, 4, 5, 18, 20, 6, 21, 5, 14, 6] with sum 205.
The numerical values for "zweihundertsieben" are [26, 23, 5, 9, 8, 21, 14, 4, 5, 18, 20, 19, 9, 5, 2, 5, 14] with sum 207.
From _Omar E. Pol_, Jun 15 2021: (Start)
-------------------------------------------------------------
   n     Name               Calculation                  a(n)
-------------------------------------------------------------
   0     Null               14 + 21 + 12 + 12           = 59
   1     Eins                5 +  9 + 14 + 19           = 47
   2     Zwei               26 + 23 +  5 +  9           = 63
   3     Drei                4 + 18 +  5 +  9           = 36
   4     Vier               22 +  9 +  5 + 18           = 54
   5     Fünf  --> Fuenf     6 + 21 +  5 + 14 +  6      = 52
   6     Sechs              19 +  5 +  3 +  8 + 19      = 54
   7     Sieben             19 +  9 +  5 +  2 +  5 + 14 = 54
   8     Acht                1 +  3 +  8 + 20           = 32
   9     Neun               14 +  5 + 21 + 14           = 54
  10     Zehn               26 +  5 +  8 + 14           = 53
  11     Elf                 5 + 12 +  6                = 23
  12     Zwölf --> Zwoelf   26 + 23 + 15 +  5 + 12 +  6 = 87
... (End)
a(16) = 88 because "sechzehn" => [19, 5, 3, 8, 26, 5, 8, 14] with sum 88, as for a(17) with "siebzehn" => [19, 9, 5, 2, 26, 5, 8, 14]. - _M. F. Hasler_, Apr 08 2023

Christian Reder, Wörter und Zahlen, Springer Verlag, Komet, Wien, 2000, p. 337.

Index entries for sequences related to German names of numbers

For analogs in other languages see A073327 (U.S. English), A169639 (French), A161406 (Spanish).

G(n, eins="eins")={my(s(n, p, z, e="ein")=n=divrem(n, p); if(n[2], Str(G(n[1]*p), G(n[2])), Str(G(n[1], e), z))); if(n<20, ["null", eins, "zwei", "drei", "vier", "fuenf", "sechs", "sieben", "acht", "neun", "zehn", "elf", "zwoelf", "dreizehn", "vierzehn", "fuenfzehn", "sechzehn", "siebzehn", "achtzehn", "neunzehn"][n+1], n<100 && n%10, Str(G(n%10, "ein"), "und", G(n\10*10)), n<100, ["zwanzig", "dreissig", "vierzig", "fuenfzig", "sechzig", "siebzig", "achtzig", "neunzig"][n\10-1], n<1000, s(n, 100, "hundert"), n<10^6, s(n, 1000, "tausend"), n<10^9, s(n, 10^6, if(n\10^6>1, " Millionen ", "e Million ")), n<10^12, s(n, 10^9, if(n\10^9>1, " Milliarden ", "e Milliarde ")))}
\\ extension to Billion, Billiarde, Trillion, Trilliarde, ... is obvious. See A007208 for a variant.
apply( {A119945(n)=vecsum([t%32|t<-Vecsmall(G(n)),t>64])}, [0..99])
\\ M. F. Hasler, Apr 08 2023

Edited by N. J. A. Sloane, Jun 10 2021

Corrected and extended by M. F. Hasler, Apr 08 2023

A152592 Consider the last letter of each of the English words zero, one, two, three, four, five, ... . Write down 0 for a vowel {a,e,i,o,u}, 1 for a consonant.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1

Offset: 0

Paul Curtz, Dec 09 2008

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,-1,1).

See A059437 for another version.

From Chai Wah Wu, Apr 18 2024: (Start)
a(n) = a(n-1) - a(n-5) + a(n-6) for n > 25.
G.f.: x^4*(x^21 - x^20 + x^17 - x^14 + x^13 - x^11 + x^10 - x^9 + x^8 - x^7 - x^2 + x - 1)/(x^6 - x^5 + x - 1). (End)

Edited by N. J. A. Sloane, Apr 09 2009, Apr 11 2009

Extended by Nathaniel Johnston, May 05 2011

A277971 a(1) = 1; a(n) > a(n-1) is the smallest number whose name in English contains the first letter of the name of a(n-1).

Original entry on oeis.org

1, 2, 3, 8, 9, 10, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 86, 87, 88, 89, 90, 91

Offset: 1

Ivan N. Ianakiev, Nov 07 2016

Cf. A277972.

name[n_]:=IntegerName[n,"Words"];a[1]=1;
a[n_]:=a[n]=Module[{i=a[n-1]+1},While[
!StringContainsQ[name[i],StringTake[name[a[n-1]],1]],i++ ];i];
a/@Range[68] (* Ivan N. Ianakiev, Dec 20 2021 *)

A277972 a(1) = 1. a(n) is the smallest unlisted number, the name of which contains the first letter of the name of a(n-1) in English.

Original entry on oeis.org

1, 2, 3, 8, 5, 4, 14, 15, 24, 10, 12, 13, 16, 6, 7, 17, 26, 18, 9, 11, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 64, 60, 61, 62, 63, 65, 66, 67, 68, 69

Offset: 1

Ivan N. Ianakiev, Nov 07 2016

Cf. A277971.

name[n_]:=IntegerName[n,"Words"];a[1]=1;
a[n_]:=a[n]=Module[{i=1}, While[Or[MemberQ[Table[a[k],{k,1,n-1}],i],
!StringContainsQ[name[i],StringTake[name[a[n-1]],1]]],i++ ];i];
a/@Range[69] (* Ivan N. Ianakiev, Dec 20 2021 *)

A345711 Lexicographically earliest sequence of distinct positive terms such that the English names of the entries form a new sequence of English names where every original entry is doubled (see the Comments section).

Original entry on oeis.org

5, 10, 20, 8, 100, 4, 7, 12, 13, 1, 19, 26, 18, 68, 69, 2, 71, 38, 6, 14, 11, 44, 9, 30, 17, 23, 24, 25, 32, 21, 28, 27, 15, 16, 22, 48, 29, 52, 31, 47, 59, 34, 36, 37, 63, 39, 40, 51, 67, 84, 126, 101, 128, 115, 76, 64, 43, 53, 83, 94, 33, 46, 82, 89, 169, 109, 93, 45, 56, 129, 99, 108, 49, 70

Offset: 1

Eric Angelini and Carole Dubois, Jun 24 2021

The first English names of the sequence are:
FIVE, TEN, TWENTY, EIGHT, ONE HUNDRED, FOUR, SEVEN, TWELVE, THIRTEEN, ONE, NINETEEN, TWENTY-SIX, EIGHTEEN, SIXTY-EIGHT, SIXTY-NINE, TWO, SEVENTY-ONE, THIRTY-EIGHT, SIX, FOURTEEN, ELEVEN, FORTY-FOUR, NINE, THIRTY, SEVENTEEN, TWENTY-THREE, TWENTY-FOUR, TWENTY-FIVE, THIRTY-TWO, TWENTY-ONE, TWENTY-EIGHT...
If we now take the 5th letter of the above English sequence (T), the 10th (E) and the 20th (N) we spell T.E.N. and 10 is the double of a(1) = 5. We then take the 8th letter of the sequence (T), the 100th (W), the 4th (E), the 7th (N), the 12th (T), the 13th (Y) to form T.W.E.N.T.Y. and 20 is the double of a(2) = 10. Etc.

Cf. A131744, A345712 (French version).

A000865 Numbers beginning with letter 'o' in English.

Original entry on oeis.org

1, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135

Offset: 1

N. J. A. Sloane

John Cerkan, Table of n, a(n) for n = 1..10000

Subsequence of A000852.

Subsequence of A131835.

Select[Range[1000],First[Characters[IntegerName[#,"Words"]]]=="o"&] (* James C. McMahon, Dec 11 2023 *)

cp's OEIS Frontend

A059093 Numbers ending with the letter "e" (in English).

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A059437 Consider the last letter of each of the English words zero, one, two, three, four, five, ... . Write down 0 for a vowel or "y", 1 for a consonant.

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A059852 Consider the English alphabet in Morse code (the International Morse radio telegraph code). Map a 'dit' to the digit one and a 'dah' to the digit 2, then express that ternary number in decimal.

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A104059 Each number is the rank in the alphabet of a letter (and "0" stands for a space). After substitution one reads (in English): "twenty twentythree five fourteen twenty twentyfive zero..." which is exactly the sequence itself (without hyphens).

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A119945 Sum of numerical values of letters in German names of the nonnegative numbers.

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A152592 Consider the last letter of each of the English words zero, one, two, three, four, five, ... . Write down 0 for a vowel {a,e,i,o,u}, 1 for a consonant.

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A277971 a(1) = 1; a(n) > a(n-1) is the smallest number whose name in English contains the first letter of the name of a(n-1).

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A277972 a(1) = 1. a(n) is the smallest unlisted number, the name of which contains the first letter of the name of a(n-1) in English.

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A345711 Lexicographically earliest sequence of distinct positive terms such that the English names of the entries form a new sequence of English names where every original entry is doubled (see the Comments section).

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A000865 Numbers beginning with letter 'o' in English.

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