A326108 - OEIS

%I #17 Jul 11 2019 14:40:56

%S 1,11,101,110,12,13,112,14,17,113,114,16,18,19,115,15,31,116,21,33,

%T 103,117,39,118,22,102,23,119,71,121,131,141,123,130,25,51,132,24,26,

%U 120,28,27,91,77,107,151,161,127,171,93,134,124,41,181,191,211,311,411,135,35,55,105,37,511,137,611,711,99

%N Lexicographically earliest sequence of distinct terms such that a(n) is divisible by two and only two digits of a(n+1).

%C The first term that does not show any digit 1 is a(20) = 33.

%H Carole Dubois, <a href="/A326108/b326108.txt">Table of n, a(n) for n = 1..5000</a>

%e The sequence starts with 1, 11, 101, 110, 12, 13, 112, 14,... and we see indeed that a(2) = 11 is the smallest available integer showing two digits that divide a(1) = 1; in the same manner we have a(3) = 101 and a(4) = 110; a(5) = 12 because 12 is the smallest available integer that has two digits dividing a(4); etc.

%o (PARI) s=0; v=1; for (n=1, 68, print1 (v", "); s+=2^v; for (w=1, oo, if (!bittest(s,w) && #select(d -> d && v%d==0, digits(w))==2, v=w; break))) \\ _Rémy Sigrist_, Jul 11 2019

%Y Cf. A326106 [a(n) is not divisible by any digit of a(n+1)], A326107 [a(n) is divisible by one and only one digit of a(n+1)], A326109  [a(n) is divisible by three and only three digits of a(n+1)] and A326110 [a(n) is divisible by four and only four digits of a(n+1)].

%K base,nonn,look

%O 1,2

%A _Eric Angelini_ and _Carole Dubois_, Jun 06 2019