10 Downing street revisited The hereunder mail was sent recently to Math-Fun. Hello Math-Fun, say we call a(n) and a(n+1) two successive terms of S, and SuperSum the sum of the digits of a(n) and a(n+1) — the SuperSum of (710;2023) is equal to 7+1+0+2+0+2+3=15. We want to build now the lexicographically earliest sequence of distinct terms > 0 such that the SuperSum of [a(n); a(n+1)] divides exactly a(n+2). If one starts S with 1 and 2, I guess we have: S = 1,2,3,5,8,13,12,7,10,16,24,26,14,39,17,20,30,15,27,45,36,… Question : Is S (not in the OEIS) a permutation of the whole numbers? (I would say yes) Hans H . was quick to correct the above sequence and commented: > EA: "S = 1, 2, 3, 5, 8, 13, 12, 7, 10, 16, 24, 26, 14, 39, 17, 20, 30, 15, 27 , 45, 36 , ..." H H >Replace 27 with 9 and 36 with 18. > EA: "Is S (not in the OEIS) a permutation of the whole numbers? (I would say yes.)" HH > I would say no. How likely are smallish numbe...