A338942 Lexicographically earliest sequence of distinct positive terms such that a(n) is present in 3*a(n+1).

1, 4, 8, 6, 2, 7, 9, 3, 10, 34, 78, 26, 42, 14, 38, 46, 82, 94, 98, 66, 22, 74, 58, 86, 62, 54, 18, 60, 20, 40, 80, 160, 534, 178, 594, 198, 660, 220, 734, 578, 526, 842, 614, 538, 846, 282, 940, 980, 1660, 5534, 5178, 1726, 5754, 1918, 6394, 8798, 6266, 5422, 8474, 6158, 5386, 8462, 6154, 8718, 2906, 4302, 1434, 478

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 17 2020

Keywords

• base
• nonn

Comments

The lexicographically earliest sequence of positive terms such that a(n) is present in 2*a(n+1) is A000351 (the powers of 5).

Conjecture: For n >= 222, a(n) = 100*a(n-16). - Jason Yuen, Dec 22 2024

Examples

			a(1) = 1 is present (as a substring) in 12 [= 3 * a(n+1) = 3 * 4];
a(2) = 4 is present in 24 (= 3 * 8);
a(3) = 8 is present in 18 (= 3 * 6);
a(4) = 6 is present in 6 (= 3 * 2); etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..270

Crossrefs

Cf. A210013, A000351.

Programs

Magma

a:=[1]; f:=func; for n in [2..70] do k:=2; while k in a or not f(a[n-1],3*k) do k:=k+1; end while; Append(~a,k); end for; a; // Marius A. Burtea, Nov 19 2020