|
| |
|
|
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.
|
|
31
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
|
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, n-1, " "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.
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
