login
A299970
Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 0, and no term occurs twice.
13
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
0,2
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
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 *)
PROG
(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}
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.
Sequence in context: A236507 A031140 A095973 * A342143 A344331 A358048
KEYWORD
nonn,base
AUTHOR
M. F. Hasler and Eric Angelini, Feb 22 2018
STATUS
approved