[math-fun] A palindrome "sum"

Hello Math-Fun, Extend S so that the cumultive sum P = a(1) +/- a(2) +/- ... +/- a(k) is always a palindrome. But remember: 1) S must be the lexicographically earliest seq of distinct terms with this propety and a(1) = 1; 2) Add the odd terms and subtract the even ones. + - + - + + - - + + - - + - + - S = 1, 3, 2, 5, 4, 19, 11, 22, 6, 17, 33, 44, 8, 41, 36, 25, 24, ... P = 1 4 2 7 3 22 33 11 5 22 55 11 3 44 8 33 9 ... Is S a permutation of the integers > 0? I guess yes -- but can't prove. (as always, forgive my errors) Best, É.