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

0,1

Comments

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

Links

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

Example

"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)

Maple

# 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

Mathematica

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 *)

Prog

(PARI) 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
(Python)
import re
from num2words import num2words
# US English
def A073327(n): return sum(ord(d)-96 for d in re.sub("\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

Crossrefs

Row sums of A073029.

For analogs in other languages see A169639 (French), A119945 (German), A161406 (Spanish).

Cf. A005589, A072922, A075831, A152611, A345126, A345157.

Sequence in context: A066539 A095390 A033384 * A169639 A252486 A188828

Adjacent sequences: A073324 A073325 A073326 * A073328 A073329 A073330

Keyword

nonn,word,look

Author

Paul Lusch, Aug 22 2002

Extensions

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

More terms from Jon E. Schoenfield, Aug 30 2009

Status

approved