A299970 - OEIS

%I #10 Mar 04 2018 19:48:16

%S 0,10,20,30,40,50,51,9,1,19,11,29,21,39,31,49,41,59,42,8,2,18,12,28,

%T 22,38,32,48,52,53,7,3,17,13,27,23,37,33,47,43,57,44,6,4,16,14,26,24,

%U 36,34,46,54,55,5,15,25,35,45,56,64,66,74,76,84,86,94,96,104

%N Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 0, and no term occurs twice.

%C It happens that from a(18) = 42 on, the sequence coincides with the "strictly positive variant" A299971. Indeed, n = 18 is the first index for which the same value occurs, and {a(n), 0 <= n < 18} = {0} U {A299971(n), 1 <= n < 18}. - _M. F. Hasler_, Feb 28 2018

%t Nest[Append[#, Block[{k = 1}, While[Nand[FreeQ[#, k], DigitCount[#[[-1]] + k, 10, 0] > 0], k++]; k]] &, {0}, 67] (* _Michael De Vlieger_, Mar 01 2018 *)

%o (PARI) a(n,f=1,d=0,a=0,u=[a])={for(n=1,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

%Y Cf. A299971 (analog with positive terms), A299957 (digit 1), A299972..A299979 (digit 2..9).

%Y Cf. A299980, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979 for an analog using multiplication: a(n)*a(n+1) has a digit 0, resp. 1, ..., resp. 9.

%K nonn,base

%O 0,2

%A _M. F. Hasler_ and _Eric Angelini_, Feb 22 2018