A132204 - OEIS

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.

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

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OFFSET

0,1

COMMENTS

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)?

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

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

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

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

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

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

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

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

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

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

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