A119945 -id:A119945 - cp's OEIS frontend

A073327 Write U.S. English name for n (ignoring hyphens and spaces) and add numerical values of letters using a=1, b=2, ..., y=25, z=26.

64, 34, 58, 56, 60, 42, 52, 65, 49, 42, 39, 63, 87, 99, 104, 65, 96, 109, 73, 86, 107, 141, 165, 163, 167, 149, 159, 172, 156, 149, 100, 134, 158, 156, 160, 142, 152, 165, 149, 142, 84, 118, 142, 140, 144, 126, 136, 149, 133, 126, 66, 100, 124, 122, 126, 108, 118

Offset: 0

Paul Lusch, Aug 22 2002

In writing out the names for these numbers, "and" is not used in U.S. English; e.g., 101 is rendered as "one hundred one" rather than "one hundred and one". - Robert Israel, Jun 12 2019
The British English version is too similar to this to have its own entry. They first differ at n=101, where here a(101) = 142, whereas in British English 101 is "one hundred and one", which is 161. - N. J. A. Sloane, Jun 09 2021
From Robert Israel's data it appears that the U.S. version has no fixed points, and the British version has exactly two fixed points, at 251 and 259. I do not know if either version has cycles of length >= 2 apart from the cycles of length 5 that are visible in A345126 and A345157. - N. J. A. Sloane, Jun 11 2021

			"One" = 15 + 14 + 5 = 34 (o is 15th letter, n is 14th letter, e is 5th letter).
From _Omar E. Pol_, Jun 15 2021: (Start)
-----------------------------------------------------
   n      Name      Calculation                  a(n)
-----------------------------------------------------
   0      Zero      26 +  5 + 18 + 15           = 64
   1      One       15 + 14 +  5                = 34
   2      Two       20 + 23 + 15                = 58
   3      Three     20 +  8 + 18 +  5 +  5      = 56
   4      Four       6 + 15 + 21 + 18           = 60
   5      Five       6 +  9 + 22 +  5           = 42
   6      Six       19 +  9 + 24                = 52
   7      Seven     19 +  5 + 22 +  5 + 14      = 65
   8      Eight      5 +  9 +  7 +  8 + 20      = 49
   9      Nine      14 +  9 + 14 +  5           = 42
  10      Ten       20 +  5 + 14                = 39
  11      Eleven     5 + 12 +  5 + 22 +  5 + 14 = 63
  12      Twelve    20 + 23 +  5 + 12 + 22 +  5 = 87
... (End)

Robert Israel, Table of n, a(n) for n = 0..10000
M. F. Hasler in reply to E. Angelini, English number words modulo themselves, SeqFan list, Jun 21 2013
Robert Israel, British English version of b-file

Row sums of A073029.
For analogs in other languages see A169639 (French), A119945 (German), A161406 (Spanish).
Cf. A005589, A072922, A075831, A152611, A345126, A345157.

# Maple program for US English
f:= proc(n) local S;
   uses StringTools;
  S:= Select(IsAlpha,convert(n,english));
  convert(map(`-`,convert(S,bytes),96),`+`)
end proc:
map(f, [$0..100]); # Robert Israel, Jun 12 2019
# British English version, valid for n < 10^9
f:= proc(n) local S;
   uses StringTools;
  S:= Select(IsAlpha, convert(n, english, And));
  convert(map(`-`, convert(S, bytes), 96), `+`)
end proc:
map(f, [$0..200]); # Robert Israel, Jun 11 2021

a[n_] := Total@ Flatten[ ToCharacterCode@# - 96 & /@ Characters@ StringDelete[IntegerName@ n, Except@ LetterCharacter]] (* after Michael De Vlieger in A362065 *); Array[a, 57, 0] (* Robert G. Wilson v, Apr 19 2023 *)

A073327(n)=sum(i=1,#n=select(t->t>64,Vec(Vecsmall(English(n)))),n[i]%32) \\ see A052360 for English(). - M. F. Hasler, Jun 22 2013

import re
from num2words import num2words
# US English
def A073327(n): return sum(ord(d)-96 for d in re.sub(r"\sand\s|[^a-z]", "", num2words(n)))
# British English
def A073327(n): return sum(ord(d)-96 for d in re.sub("[^a-z]", "", num2words(n, lang='en_GB'))) # Chai Wah Wu, Jun 13 2021

a(0) added by N. J. A. Sloane, Jun 30 2008

More terms from Jon E. Schoenfield, Aug 30 2009

A169639 Write n in French (cf. A167507) and sum the letters using a=1, ..., z=26.

Original entry on oeis.org

64, 35, 54, 81, 82, 43, 52, 60, 58, 46, 37, 60, 71, 83, 123, 92, 64, 97, 95, 83, 72, 132, 126, 153, 154, 115, 124, 132, 130, 118, 82, 142, 136, 163, 164, 125, 134, 142, 140, 128, 97, 157, 151, 178, 179, 140, 149, 157, 155, 143, 104, 164, 158, 185, 186, 147, 156, 164

Offset: 0

Jacques ALARDET, Apr 04 2010

Accents are ignored. - Chai Wah Wu, Jun 11 2021

			From _Omar E. Pol_, Jun 15 2021: (Start)
-----------------------------------------------------
   n      Name      Calculation                  a(n)
-----------------------------------------------------
   0      Zero      26 +  5 + 18 + 15           = 64
   1      Un        21 + 14                     = 35
   2      Deux       4 +  5 + 21 + 24           = 54
   3      Trois     20 + 18 + 15 +  9 + 19      = 81
   4      Quatre    17 + 21 +  1 + 20 + 18 +  5 = 82
   5      Cinq       3 +  9 + 14 + 17           = 43
   6      Six       19 +  9 + 24                = 52
   7      Sept      19 +  5 + 16 + 20           = 60
   8      Huit       8 + 21 +  9 + 20           = 58
   9      Neuf      14 +  5 + 21 +  6           = 46
  10      Dix        4 +  9 + 24                = 37
  11      Onze      15 + 14 + 26 +  5           = 60
  12      Douze      4 + 15 + 21 + 26 +  5      = 71
... (End)

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Cf. A167507, A169641 ("limit points").

For other languages see A073327 (U.S. English), A119945 (German), A161406 (Spanish).

A169639(n)=vecsum([t%32|t<-Vecsmall(French(n)),t>64]) \\ Cf. A167507 for French(). - M. F. Hasler, Apr 08 2023

from num2words import num2words
from unidecode import unidecode
def A169639(n): return sum(ord(s)-96 for s in unidecode(num2words(n,lang='fr')) if s.isalpha()) # Chai Wah Wu, Jun 11 2021

Edited by N. J. A. Sloane, Apr 05 2010

Offset corrected by Mohammed Yaseen, Jun 11 2021

A161406 Write the Spanish name for n (ignoring spaces) and add numerical values of letters using a=1, b=2, ..., ñ=15, ..., y=26, z=27, n >= 0.

Original entry on oeis.org

43, 52, 40, 65, 82, 45, 54, 60, 43, 69, 45, 38, 28, 53, 68, 71, 84, 90, 73, 99, 77, 133, 121, 146, 163, 126, 135, 141, 124, 150, 90, 168, 156, 181, 198, 161, 170, 176, 159, 185, 86, 164, 152, 177, 194, 157, 166, 172, 155, 181, 92, 170, 158, 183, 200, 163, 172, 178, 161

Offset: 0

Claudio Meller, Jun 09 2009

Spanish has one more letter than English: ñ is the 15th letter.

			From _Omar E. Pol_, May 10 2021: (Start)
----------------------------------------------------
   n      Name     Calculation                  a(n)
----------------------------------------------------
   0      Cero      3 +  5 + 19 + 16           = 43
   1      Uno      22 + 14 + 16                = 52
   2      Dos       4 + 16 + 20                = 40
   3      Tres     21 + 19 +  5 + 20           = 65
   4      Cuatro    3 + 22 +  1 + 21 + 19 + 16 = 82
   5      Cinco     3 +  9 + 14 +  3 + 16      = 45
   6      Seis     20 +  5 +  9 + 20           = 54
   7      Siete    20 +  9 +  5 + 21 +  5      = 60
   8      Ocho     16 +  3 +  8 + 16           = 43
   9      Nueve    14 + 22 +  5 + 23 +  5      = 69
  10      Diez      4 +  9 +  5 + 27           = 45
  11      Once     16 + 14 +  3 +  5           = 38
  12      Doce      4 + 16 +  3 +  5           = 28
... (End)

For analogs in other languages see A073327 (U.S. English), A169639 (French), A119945 (German).

Name edited and offset corrected by Omar E. Pol, Jun 10 2021

A226911 Remainder modulo n of the sum of the letters of the English word(s) for n (A073327: a=1, ..., z=26).

Original entry on oeis.org

0, 0, 2, 0, 2, 4, 2, 1, 6, 9, 8, 3, 8, 6, 5, 0, 7, 1, 10, 7, 15, 11, 2, 23, 24, 3, 10, 16, 4, 10, 10, 30, 24, 24, 2, 8, 17, 35, 25, 4, 36, 16, 11, 12, 36, 44, 8, 37, 28, 16, 49, 20, 16, 18, 53, 6, 17, 57, 49, 37, 9, 31, 27, 29, 9, 17, 28, 10, 1, 40, 2, 24, 20, 22, 2, 10, 21, 3

Offset: 1

Eric Angelini and M. F. Hasler, Jun 22 2013

By definition, a(n) < n so iterated application of this function to any initial value n will create a strictly decreasing sequence ending in 0.

Robert Israel, Table of n, a(n) for n = 1..10000
M. Hasler in reply to E. Angelini, English number words modulo themselves, SeqFan list, Jun 21 2013

Cf. A073029, A119945, A072922, A075831, A152611, A052360, A362065.

f:= proc(n) local S;
   uses StringTools;
  S:= Select(IsAlpha,convert(n,english));
  convert(map(`-`,convert(S,bytes),96),`+`) mod n
end proc:
map(f, [$1..100]); # Robert Israel, Jun 12 2019

a[n_] := Mod[Total@ Flatten[ ToCharacterCode[#] - 96 & /@ Characters@ StringDelete[ IntegerName[n], Except@ LetterCharacter]], n] (* after Michael De Vlieger in A362065 *); Array[a, 78] (* Robert G. Wilson v, Apr 22 2023 *)

PARI
```
A226911 = n->A073327(n)%n
```

a(n) = A073327(n) mod n.

It appears that a(n) = A073327(n) for n > 279. - Robert Israel, Jun 12 2019

A226942 Number of iterations of A226911 until 0 is reached, for starting value n.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 2, 2, 3, 4, 3, 3, 3, 3, 3, 1, 3, 2, 5, 3, 4, 4, 2, 3, 4, 3, 5, 2, 2, 5, 5, 6, 4, 4, 2, 3, 4, 3, 5, 2, 4, 2, 4, 4, 4, 5, 3, 5, 3, 2, 4, 4, 2, 3, 3, 3, 4, 5, 4, 5, 4, 6, 6, 3, 4, 4, 3, 5, 2, 3, 2, 4, 4, 5, 2, 5, 5, 3, 5, 6, 6, 3, 4

Offset: 1

M. F. Hasler, Jun 23 2013

Iterating the map A226911 was suggested in the SeqFan post by E. Angelini, cf link.

Robert Israel, Table of n, a(n) for n = 1..10000
M. Hasler in reply to E. Angelini, English number words modulo themselves, SeqFan list, Jun 21 2013

Cf. A073327, A073029, A119945, A072922, A075831, A152611, A052360.

f:= proc(n) local S;
  uses StringTools;
  S:= Select(IsAlpha, convert(n, english));
  convert(map(`-`, convert(S, bytes), 96), `+`) mod n
end proc:
g:= proc(n) option remember;
    local v;
    v:= f(n);
    1+procname(v)
end proc:
g(0):= 0:
map(g, [$1..100]); # Robert Israel, Jun 13 2019

A226942 = n -> for(c=1,9e9,(n=A226911(n))||return(c))

A119946 Final digit sum of numerical values of German names of the nonnegative numbers.

Original entry on oeis.org

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

Offset: 0

Wolfdieter Lang, Jul 20 2006

The first digits sums are given in A119945.

Umlaute are taken as ``ae'' (not appearing), ``oe'', ``ue'' and ``sz'' (scharp s) (like in the German name for ``30'') as ``ss'' (not "sz").

			``Null'' in German for the number 0 has first digit sum
59=A119945(0). Therefore the next digit sum becomes 5+9=14 and finally
1+4=5, hence a(0)=5.

cp's OEIS Frontend

A073327 Write U.S. English name for n (ignoring hyphens and spaces) and add numerical values of letters using a=1, b=2, ..., y=25, z=26.

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A169639 Write n in French (cf. A167507) and sum the letters using a=1, ..., z=26.

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A161406 Write the Spanish name for n (ignoring spaces) and add numerical values of letters using a=1, b=2, ..., ñ=15, ..., y=26, z=27, n >= 0.

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A226911 Remainder modulo n of the sum of the letters of the English word(s) for n (A073327: a=1, ..., z=26).

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A226942 Number of iterations of A226911 until 0 is reached, for starting value n.

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A119946 Final digit sum of numerical values of German names of the nonnegative numbers.

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