A121711 Lexicographically smallest permutation of the natural numbers such that GCD(s(k-1)+1,a(k)) greater than GCD(s(k-1),a(k)+1), where s is the sum of preceding terms (A121712); a(1)=1.

1, 2, 4, 8, 6, 10, 12, 11, 15, 5, 3, 9, 18, 14, 7, 16, 22, 20, 23, 21, 19, 13, 24, 26, 25, 30, 35, 28, 32, 34, 36, 38, 40, 42, 39, 52, 33, 27, 45, 46, 48, 44, 41, 50, 43, 54, 56, 58, 60, 62, 55, 49, 51, 57, 63, 17, 64, 66, 61, 31, 68, 65, 69, 59, 37, 70, 72, 76, 53, 47, 74, 78