A299979 Lexicographic first sequence of positive integers such that a(n) + a(n+1) has a digit 9, and no term occurs twice.

1, 8, 11, 18, 21, 28, 31, 38, 41, 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, 49, 10, 9, 20, 19, 30, 29, 40, 39, 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, 55

Offset

1,2

Comments

A permutation of the positive integers.

It happens that from a(50) = 50 on, this sequence coincides with the variant A299969 (which starts at 0 and has nonnegative terms). Indeed the two sequences have the property that the terms a(1..49) resp. A299969(0..49) exactly contain all numbers from 1 to 49, respectively 0 to 49. - 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[#[[-1]] + k, 10, 9] > 0], k++]; k]] &, {1}, 90] (* Michael De Vlieger, Mar 01 2018 *)

Prog

(PARI) a(n, f=1, d=9, 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. A299969 (analog with nonnegative terms), A299957 (analog with digit 1), A299971, A299972, ..., A299978 (digit 0, 2, ..., 8).

Sequence in context: A111254 A127271 A118549 * A291663 A306277 A067469

Adjacent sequences: A299976 A299977 A299978 * A299980 A299981 A299982

Keyword

nonn,base

Author

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

Status

approved