cp's OEIS Frontend

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

%I A226911 #24 Dec 23 2024 14:53:43
%S A226911 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,
%T A226911 10,30,24,24,2,8,17,35,25,4,36,16,11,12,36,44,8,37,28,16,49,20,16,18,
%U A226911 53,6,17,57,49,37,9,31,27,29,9,17,28,10,1,40,2,24,20,22,2,10,21,3
%N A226911 Remainder modulo n of the sum of the letters of the English word(s) for n (A073327: a=1, ..., z=26).
%C A226911 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.
%H A226911 Robert Israel, <a href="/A226911/b226911.txt">Table of n, a(n) for n = 1..10000</a>
%H A226911 M. Hasler in reply to E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-June/011350.html">English number words modulo themselves</a>, SeqFan list, Jun 21 2013
%F A226911 a(n) = A073327(n) mod n.
%F A226911 It appears that a(n) = A073327(n) for n > 279. - _Robert Israel_, Jun 12 2019
%p A226911 f:= proc(n) local S;
%p A226911    uses StringTools;
%p A226911   S:= Select(IsAlpha,convert(n,english));
%p A226911   convert(map(`-`,convert(S,bytes),96),`+`) mod n
%p A226911 end proc:
%p A226911 map(f, [$1..100]); # _Robert Israel_, Jun 12 2019
%t A226911 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 *)
%o A226911 (PARI) A226911 = n->A073327(n)%n
%Y A226911 Cf. A073029, A119945, A072922, A075831, A152611, A052360, A362065.
%K A226911 nonn,word,look
%O A226911 1,3
%A A226911 _Eric Angelini_ and _M. F. Hasler_, Jun 22 2013