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A299969
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Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 9, and no term occurs twice.
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21
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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}
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CROSSREFS
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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.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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