A226911 -id:A226911 - cp's OEIS frontend

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

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))

A362065 Write the English name of a(n); sum the ranks of its letters in the alphabet; divide the sum by a(n); the result is an integer.

Original entry on oeis.org

1, 2, 4, 16, 134

Offset: 1

Eric Angelini and Mensanator, Apr 07 2023

Is a(5) = 134 the last such term?
Indices of zeros in A226911; and conjectured finite, full based on an observation there. - Michael S. Branicky, Apr 07 2023
If a(6) exists, it is > 10^7. - Robert G. Wilson v, Apr 22 2023
There are no more terms because for any number k > 10^6, the sum of the ranks of the letters in the English name of k will be far less than k. - Erich Friedman, Nov 13 2024

			a(1) = 1 = ONE and O+N+E = 34 and 34/1 = 34;
a(2) = 2 = TWO and T+W+O = 58 and 58/2 = 29;
a(3) = 4 = FOUR and F+O+U+R = 60 and 60/4 = 15;
a(4) = 16 = SIXTEEN and S+I+X+T+E+E+N = 96 and 96/16 = 6; etc.

Cf. A092320, A126259, A073327, A226911.

Position[Array[Mod[Total@ Flatten[ToCharacterCode[#] - 96 & /@ Characters@ StringDelete[IntegerName[#], Except@ LetterCharacter]], #] &, 10^4] , 0][[All, 1]] (* Michael De Vlieger, Apr 07 2023 *)

cp's OEIS Frontend

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

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