

A235538


Earliest infinite sequence of natural numbers such that the members of this sequence as well as the absolute values of the members of the kth differences of this sequence, for all k>0, are all distinct.


3



1, 3, 9, 26, 5, 13, 31, 15, 27, 81, 22, 45, 92, 20, 50, 145, 46, 89, 32, 71, 151, 40, 75, 163, 73, 124, 60, 126, 244, 97, 219, 63, 132, 306, 68, 144, 297, 79, 166, 354, 83, 187, 394, 94, 203, 419, 108, 220, 460, 127, 260, 110, 247, 513, 161, 340, 117, 252
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, n1]; m0 = 1; While[ MemberQ[ diffs0, m0], m0++]; For[m = m0, True, m++, am = Append[aa, m]; td = Table[Differences[am, k], {k, 0, n1}]; 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}] (* JeanFrançois Alcover, Jan 31 2018 *)


PROG

(Perl) See Link section.


CROSSREFS

Cf. A005228, A005282, A035312, A235539, A327460, A327887.
Sequence in context: A013572 A119851 A119825 * A218916 A037260 A035313
Adjacent sequences: A235535 A235536 A235537 * A235539 A235540 A235541


KEYWORD

nonn,nice


AUTHOR

Paul Tek, Jan 12 2014


EXTENSIONS

Added "infinite" to definition.  N. J. A. Sloane, Oct 05 2019


STATUS

approved



