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A299969 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 9, and no term occurs twice. 21
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler and Eric Angelini, Feb 22 2018
STATUS
approved

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Last modified March 29 05:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)