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

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

Author

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

Keywords

• nonn
• word
• look

Comments

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.

Links

• 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

Crossrefs

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

Programs

Maple

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

Mathematica

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

Formula

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

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