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

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

Offset

0,2

Comments

A permutation of the nonnegative integers.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Mathematica

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 *)

Prog

(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}

Crossrefs

Cf. A299979 (analog with positive terms), A299957 (analog with digit 1), A299970, A299982, ..., A299988 (digit 0, 2, ..., 8).

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: A141640 A231504 A298979 * A050551 A022099 A042113

Adjacent sequences: A299966 A299967 A299968 * A299970 A299971 A299972

Keyword

nonn,base

Author

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

Status

approved