

A299970


Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 0, and no term occurs twice.


13



0, 10, 20, 30, 40, 50, 51, 9, 1, 19, 11, 29, 21, 39, 31, 49, 41, 59, 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
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OFFSET

0,2


COMMENTS

It happens that from a(18) = 42 on, the sequence coincides with the "strictly positive variant" A299971. Indeed, n = 18 is the first index for which the same value occurs, and {a(n), 0 <= n < 18} = {0} U {A299971(n), 1 <= n < 18}.  M. F. Hasler, Feb 28 2018


LINKS

Table of n, a(n) for n=0..67.


MATHEMATICA

Nest[Append[#, Block[{k = 1}, While[Nand[FreeQ[#, k], DigitCount[#[[1]] + k, 10, 0] > 0], k++]; k]] &, {0}, 67] (* Michael De Vlieger, Mar 01 2018 *)


PROG

(PARI) a(n, f=1, d=0, a=0, u=[a])={for(n=1, n, f&&if(f==1, print1(a", "), write(f, n1, " "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. A299971 (analog with positive terms), A299957 (digit 1), A299972..A299979 (digit 2..9).
Cf. A299980, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979 for an analog using multiplication: a(n)*a(n+1) has a digit 0, resp. 1, ..., resp. 9.
Sequence in context: A236507 A031140 A095973 * A037997 A044850 A282150
Adjacent sequences: A299967 A299968 A299969 * A299971 A299972 A299973


KEYWORD

nonn,base


AUTHOR

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


STATUS

approved



