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A299969 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 9, and no term occurs twice. 21

%I

%S 0,9,10,19,20,29,30,39,40,49,41,8,1,18,11,28,21,38,31,48,42,7,2,17,12,

%T 27,22,37,32,47,43,6,3,16,13,26,23,36,33,46,44,5,4,15,14,25,24,35,34,

%U 45,50,59,60,69,70,79,80,89,90,99,91,58,51,68,61,78,71,88,81,98,92,57,52,67,62,77,72,87,82,97,93,56,53,66,63,76,73,86,83,96,94

%N Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 9, and no term occurs twice.

%C A permutation of the nonnegative integers.

%C It happens that from a(50) = 50 on, this sequence coincides with the variant A299979 (starting at 1 and having only positive terms). Indeed the two sequences have the property that the terms a(0..49) resp. A299979(1..49) exactly contain all numbers from 0 to 49, respectively 1 to 49. - _M. F. Hasler_, Feb 28 2018

%H Vincenzo Librandi, <a href="/A299969/b299969.txt">Table of n, a(n) for n = 0..2000</a>

%t Nest[Append[#, Block[{k = 1}, While[Nand[FreeQ[#, k], DigitCount[#[[-1]] + k, 10, 9] > 0], k++]; k]] &, {0}, 90] (* _Michael De Vlieger_, Mar 01 2018 *)

%o (PARI) a(n,f=1,d=9,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. A299979 (analog with positive terms), A299957 (analog with digit 1), A299970, A299982, ..., A299988 (digit 0, 2, ..., 8).

%Y Cf. A299980, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979 for the 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

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)