[math-fun] A word sequence

Hello Math-Fun, [and J.-M. Falcoz for a possible French version], here is an English word sequence, for a change: S=7,5,7,4,2,-16,1,-22,-22,-22,-26,0,0,-31,-31,-6,-3,-37,-38,-37,-7,-8,... If you now compute k= |n+a(n)| the result k is the number of letters used in English to write the integers « n » and « a(n) ». Example for n=1: k = |1 + a(1)| = |1+7| = 8 = {ONE,SEVEN} For n=2 we have: k = |2 + a(2)| = |2+5| = 7 = {TWO,FIVE} For n = 3: k = |3+a(3)| = |3+7| = 10 = {THREE,SEVEN} ... For n=6: k = |6+a(6)| = |6-16| = 10 = {SIX,SIXTEEN} etc. When a(n) = 0, there is (apparently) no solution [see a(12) and a(13)]. We’d like S to be the lexicographically earliest seq with this property. Best, É.