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

Author

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

Keywords

• nonn
• base

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

Crossrefs

Cf. A299969 (analog with nonnegative terms), A299957 (analog with digit 1), A299971, A299972, ..., A299978 (digit 0, 2, ..., 8).

Programs

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 *)

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}