A299970 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 0, and no term occurs twice.

0, 10, 20, 30, 40, 50, 51, 9, 1, 19, 11, 29, 21, 39, 31, 49, 41, 59, 42, 8, 2, 18, 12, 28, 22, 38, 32, 48, 52, 53, 7, 3, 17, 13, 27, 23, 37, 33, 47, 43, 57, 44, 6, 4, 16, 14, 26, 24, 36, 34, 46, 54, 55, 5, 15, 25, 35, 45, 56, 64, 66, 74, 76, 84, 86, 94, 96, 104

Offset: 0

Author

M. F. Hasler and Eric Angelini, Feb 22 2018

Keywords

• nonn
• base

Comments

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

Crossrefs

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

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.

Programs

Mathematica

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 *)

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}