OFFSET
1,2
LINKS
Paul Tek, Table of n, a(n) for n = 1..1000
Paul Tek, PERL program for this sequence
EXAMPLE
For n=1:
- 1 is admissible; hence a(1)=1.
For n=2:
- 1 is not admissible (as it already appears in the sequence),
- 2 is not admissible (as a(1) would appear in the first differences),
- 3 is admissible; hence a(2)=3.
For n=3:
- 1 is not admissible (as it already appears in the sequence),
- 2 is not admissible (as it already appears in the first differences),
- 3 is not admissible (as it already appears in the sequence),
- 4 is not admissible (as a(1) would appear in the first differences),
- 5 is not admissible (as 2 would appear twice in the first differences),
- 6 is not admissible (as a(2) would appear in the first differences),
- 7 is not admissible (as 2 would appear in the first and second differences),
- 8 is not admissible (as a(2) would appear in the second differences),
- 9 is admissible; hence a(3)=9.
MATHEMATICA
a[1] = 1; diffs0 = {1} (* flattened array of successive differences *);
a[n_] := a[n] = Module[{}, aa = Array[a, n-1]; m0 = 1; While[ MemberQ[ diffs0, m0], m0++]; For[m = m0, True, m++, am = Append[aa, m]; td = Table[Differences[am, k], {k, 0, n-1}]; diffs = Abs[Flatten[td]]; If[ Length[diffs] == Length[Union[diffs]], diffs0 = diffs//Sort; Return[m]]] ];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 31 2018 *)
PROG
(Perl) See Link section.
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Paul Tek, Jan 12 2014
EXTENSIONS
Added "infinite" to definition. - N. J. A. Sloane, Oct 05 2019
STATUS
approved