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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.
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%I #5 Mar 30 2012 18:40:43

%S 2341,351,0,940,0,296,81,665,1011,431,500

%N 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 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 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 a(0) = A132475(ZERO) = A132475(Z)+A132475(E)+A132475(R)+A132475(O) = 2000 + 250 + 80 + 11 = 2341.

%e a(1) = A132475(ONE) = A132475(O)+A132475(N)+A132475(E) = 11 + 90 + 250 = 351.

%e a(2) = 0 because "TWO" contains a "W" which is not one of Tartaglia's letters.

%e a(3) = A132475(THREE) = 160 + 200 + 80 + 250 + 250 = 940.

%e a(4) = 0 because "FOUR" contains a "U" which is not one of Tartaglia's letters.

%e a(5) = A132475(FIVE) = 40 + 1 + 5 + 250 = 296.

%e a(6) = A132475(SIX) = 70 + 1 + 10 = 81.

%e a(7) = A132475(SEVEN) = 70 + 250 + 5 + 250 + 90 = 665.

%e a(8) = A132475(EIGHT) = 250 + 1 + 400 + 200 + 160 = 1011.

%e a(9) = A132475(NINE) = 90 + 1 + 90 + 250 = 431.

%e a(10) = A132475(TEN) = 160 + 250 + 90 = 500 = A132475(Q).

%Y Cf. A005589, A052360, A052362-A052363, A134629, A132475.

%K nonn,word

%O 0,1

%A _Jonathan Vos Post_, Nov 19 2007