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A258136
Lexicographically earliest sequence of odd positive integers such that the terms and their absolute first differences are all distinct.
2
1, 3, 7, 13, 5, 15, 27, 9, 23, 39, 11, 31, 53, 17, 41, 67, 19, 49, 81, 21, 55, 93, 25, 65, 107, 29, 73, 119, 33, 83, 135, 35, 89, 145, 37, 95, 157, 43, 109, 45, 115, 187, 47, 121, 197, 51, 131, 213, 57, 141, 229, 59, 149, 241, 61, 155, 251, 63, 161, 263, 69
OFFSET
1,2
LINKS
Eric Angelini, Derangements on the SeqFan list, May 21 2015.
FORMULA
a(n) = 2*A081145(n)-1.
MAPLE
b:= proc() false end:
a:= proc(n) option remember; local k;
if n=1 then b(1):= true; 1
else a(n-1); for k while b(k) or
b(abs(a(n-1)-k)) by 2 do od;
b(k), b(abs(a(n-1)-k)):= true$2; k
fi
end:
seq(a(n), n=1..101);
MATHEMATICA
b[_] = False;
a[n_] := a[n] = Module[{k},
If[n == 1, b[1] = True; 1,
a[n-1]; For[k = 1, b[k] ||
b[Abs[a[n-1] - k]], k += 2];
{b[k], b[Abs[a[n-1] - k]]} = {True, True}; k]];
Table[a[n], {n, 1, 101}] (* Jean-François Alcover, Aug 01 2021, after Alois P. Heinz *)
CROSSREFS
Cf. A081145, A258137 (absolute first differences), A257941, A257944.
Sequence in context: A346154 A010260 A366999 * A209387 A128156 A108768
KEYWORD
nonn
AUTHOR
Eric Angelini and Alois P. Heinz, May 21 2015
STATUS
approved