

A299957


The sum a(n) + a(n+1) always has at least one digit "1". Lexicographically first such sequence of nonnegative integers without duplicate term.


30



0, 1, 9, 2, 8, 3, 7, 4, 6, 5, 10, 11, 20, 21, 30, 31, 40, 41, 50, 51, 49, 12, 19, 22, 29, 32, 39, 42, 58, 13, 18, 23, 28, 33, 38, 43, 48, 52, 53, 47, 14, 17, 24, 27, 34, 37, 44, 56, 15, 16, 25, 26, 35, 36, 45, 46, 54, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80
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OFFSET

0,3


COMMENTS

The sequence starts with a(0) = 0 and is always extended with the smallest integer not yet present that does not lead to a contradiction. The sequence is a permutation of the natural numbers.
Originally the sequence was defined starting with a(1) = 1 and using only positive integers. This leads to the same sequence restricted to positive indices, which yields a permutation of the positive integers.  M. F. Hasler, Feb 28 2018


LINKS

M. F. Hasler, Table of n, a(n) for n = 0..10000


EXAMPLE

1 + 9 = 10; 9 + 2 = 11; 2 + 8 = 10; 8 + 3 = 11; 3 + 7 = 10; 7 + 4 = 11; 4 + 6 = 10; 6 + 5 = 11; etc.


MATHEMATICA

Nest[Append[#, Block[{k = 1}, While[Nand[FreeQ[#, k], DigitCount[k + #[[1]], 10, 1] > 0], k++]; k]] &, {1}, 98] (* Michael De Vlieger, Feb 22 2018 *)


PROG

(PARI) a(n, f=1, a=0, u=[a])={for(n=a+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)), 1)&&(a=k)&&break); u=setunion(u, [a]); u[2]==u[1]+1&&u=u[^1]); a} \\ M. F. Hasler, Feb 22 2018


CROSSREFS

Cf. A299952 (different constraint: a(n) + a(n+1) must be substring of concatenation of a(1..n+1)).
Cf. A299970, A299982, ..., A299988, A299969 (nonnegative analog with digit 0, 2, ..., 9), A299971, A299972, ..., A299979 (positive analog with digit 0, 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: A298514 A343215 A137301 * A252001 A098784 A105172
Adjacent sequences: A299954 A299955 A299956 * A299958 A299959 A299960


KEYWORD

nonn,base


AUTHOR

Eric Angelini, Feb 22 2018


EXTENSIONS

Extended to a(0) = 0 by M. F. Hasler, Feb 28 2018


STATUS

approved



