A269363 Lexicographically first injection of natural numbers beginning with a(1)=3 such that for all n >= 1, a(n)*a(n+1) is a fibbinary number (A003714), i.e., has no adjacent 1's in its base-2 representation.

3, 6, 7, 12, 11, 15, 22, 24, 14, 19, 27, 38, 28, 23, 46, 48, 43, 30, 39, 35, 59, 44, 31, 75, 62, 87, 51, 83, 56, 47, 88, 54, 76, 55, 96, 86, 60, 71, 67, 70, 78, 112, 79, 107, 102, 91, 120, 139, 118, 140, 119, 142, 131, 134, 155, 240, 156, 135, 152, 108, 95, 92, 103, 179, 184, 115, 147, 224, 94, 175, 123, 150, 111, 158, 214, 163, 203

Offset: 1

Author

Antti Karttunen, Feb 25 2016

Keywords

• nonn
• base
• look

Comments

The sequence is conjectured to be a permutation of A091067.

The scatter plot is quite interesting (essentially the same as A269367). Compare also to the graph of A269361.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003714, A003987, A091067, A266121, A266191, A269361, A269365, A269366.

Cf. A269367 (the terms ranked with A255070).

Programs

Mathematica

fibbinaryQ[n_] := BitAnd[n, 2 n]==0; a[1]=3; a[n_] := a[n] = For[k=1, True, k++, If[Mod[k, 4] != 1, If[fibbinaryQ[a[n-1] k], If[FreeQ[Array[a, n-1], k], Return[k]]]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 02 2016 *)