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 A299971 Lexicographic first sequence of positive integers such that a(n) + a(n+1) has a digit 0, and no term occurs twice. 10
 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 50, 10, 20, 30, 40, 60, 42, 8, 2, 18, 12, 28, 22, 38, 32, 48, 52, 53, 7, 3, 17, 13, 27, 23, 37, 33, 47, 43, 57, 44, 6, 4, 16, 14, 26, 24, 36, 34, 46, 54, 55, 5, 15, 25, 35, 45, 56, 64, 66, 74, 76, 84, 86, 94, 96, 104, 97 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It happens that from a(18) = 42 on, the sequence coincides with the "nonnegative variant" A299970. Indeed, n = 18 is the first index for which the same value occurs, and {a(n), 1 <= n < 18} U {0} = {A299970(n), 0 <= n < 18}. - 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[k + #[[-1]], 10, 0] > 0], k++]; k]] &, {1}, 67] (* Michael De Vlieger, Feb 22 2018 *) PROG (PARI) a(n, f=1, d=0, 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. A299970 (analog with nonnegative terms), A299957 (analog with digit 1), A299972 .. A299979 (digit 2..9). 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: A137018 A182391 A263722 * A090771 A329279 A284295 Adjacent sequences:  A299968 A299969 A299970 * A299972 A299973 A299974 KEYWORD nonn,base AUTHOR M. F. Hasler and Eric Angelini, Feb 22 2018 STATUS approved

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Last modified December 8 02:30 EST 2019. Contains 329850 sequences. (Running on oeis4.)