cp's OEIS Frontend

A132204 Sum of the numerical equivalents for the 23 Latin letters, according to Tartaglia, of the letters in the English name of n, excluding spaces and hyphens.

%I A132204 #5 Mar 30 2012 18:40:43
%S A132204 2341,351,0,940,0,296,81,665,1011,431,500
%N A132204 Sum of the numerical equivalents for the 23 Latin letters, according to Tartaglia, of the letters in the English name of n, excluding spaces and hyphens.
%C A132204 Which are the fixed points n such that a(n) = n? Which n have prime a(n)? What are the equivalence classes of integers that have the same a(n)? Which n divide a(n)? Which n have a(n) that can be read as binary, as with a(8) = 1011? What is the sequence of n such that a(n) = 0 (i.e. the English name on n contains a J, U, or W)?
%C A132204 This sequence seems unnatural, since English uses three letters that were not in the Latin alphabet (W, U, J). A better sequence would first write the names of the numbers in Latin (cf. A132984) and then sum the values of the letters. - _N. J. A. Sloane_, Nov 30 2007
%e A132204 a(0) = A132475(ZERO) = A132475(Z)+A132475(E)+A132475(R)+A132475(O) = 2000 + 250 + 80 + 11 = 2341.
%e A132204 a(1) = A132475(ONE) = A132475(O)+A132475(N)+A132475(E) = 11 + 90 + 250 = 351.
%e A132204 a(2) = 0 because "TWO" contains a "W" which is not one of Tartaglia's letters.
%e A132204 a(3) = A132475(THREE) = 160 + 200 + 80 + 250 + 250 = 940.
%e A132204 a(4) = 0 because "FOUR" contains a "U" which is not one of Tartaglia's letters.
%e A132204 a(5) = A132475(FIVE) = 40 + 1 + 5 + 250 = 296.
%e A132204 a(6) = A132475(SIX) = 70 + 1 + 10 = 81.
%e A132204 a(7) = A132475(SEVEN) = 70 + 250 + 5 + 250 + 90 = 665.
%e A132204 a(8) = A132475(EIGHT) = 250 + 1 + 400 + 200 + 160 = 1011.
%e A132204 a(9) = A132475(NINE) = 90 + 1 + 90 + 250 = 431.
%e A132204 a(10) = A132475(TEN) = 160 + 250 + 90 = 500 = A132475(Q).
%Y A132204 Cf. A005589, A052360, A052362-A052363, A134629, A132475.
%K A132204 nonn,word
%O A132204 0,1
%A A132204 _Jonathan Vos Post_, Nov 19 2007