A362065 -id:A362065 - 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

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

A362092 Write the English name of a(n); concatenate the ranks of its letters in the alphabet; divide the concatenation by a(n); the result is an integer.

Original entry on oeis.org

1, 5, 25, 45, 46, 54, 111, 195, 295, 355, 3325, 4245, 7225, 11933, 115075, 359789, 761028, 962043, 1013845, 2281588, 3940925, 14387257, 90130513, 265601357, 490538725, 904759878, 1140058418, 1259245865, 1490515166, 1619293314

Offset: 1

Eric Angelini, Apr 08 2023

			a(1) = 1, O.N.E, 15.14.5 and 15145/1 = 15145 with remainder 0;
a(2) = 5, F.I.V.E, 6.9.22.5 and 69225/5 = 13845 with remainder 0; etc.

Cf. A362065.

from num2words import num2words
def rankcat(n):
    return int("".join(str(ord(c)-96) for c in num2words(n).replace(" and", "") if c.isalpha()))
def ok(n):
    return n and rankcat(n)%n == 0
print([k for k in range(1000) if ok(k)]) # Michael S. Branicky, Apr 08 2023

a(14)-a(23) from Michael S. Branicky, Apr 08 2023

a(24)-a(30) from Tejas Sah, Oct 17 2024

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A362092 Write the English name of a(n); concatenate the ranks of its letters in the alphabet; divide the concatenation by a(n); the result is an integer.

Views

Author

Keywords

Examples

Crossrefs

Programs

Python

Extensions