A299971 Lexicographic first sequence of positive integers such that a(n) + a(n+1) has a digit 0, and no term occurs twice.

1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 50, 10, 20, 30, 40, 60, 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, 97

Offset

1,2

Comments

It happens that from a(18) = 42 on, the sequence coincides with the "nonnegative variant" A299970. Indeed, n = 18 is the first index for which the same value occurs, and {a(n), 1 <= n < 18} U {0} = {A299970(n), 0 <= n < 18}. - M. F. Hasler, Feb 28 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Mathematica

Nest[Append[#, Block[{k = 1}, While[Nand[FreeQ[#, k], DigitCount[k + #[[-1]], 10, 0] > 0], k++]; k]] &, {1}, 67] (* Michael De Vlieger, Feb 22 2018 *)

Prog

(PARI) a(n, f=1, d=0, a=1, u=[a])={for(n=2, 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. A299970 (analog with nonnegative terms), A299957 (analog with digit 1), A299972 .. A299979 (digit 2..9).

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.

Sequence in context: A182391 A346465 A263722 * A090771 A329279 A372242

Adjacent sequences: A299968 A299969 A299970 * A299972 A299973 A299974

Keyword

nonn,base

Author

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

Status

approved