A329389 Solution sequence (a(n)) of the complementary equation a(n) = 6 b(n+1) - b(n), with b(0) = 1.

11, 16, 21, 26, 31, 36, 41, 46, 51, 62, 66, 71, 76, 87, 91, 96, 101, 112, 116, 121, 126, 137, 141, 146, 151, 162, 166, 171, 176, 187, 191, 196, 201, 212, 216, 221, 226, 237, 241, 246, 251, 262, 266, 271, 276, 281, 286, 291, 296, 301, 306, 317, 321, 326, 337

Offset

0,1

Comments

The conditions that (a(n)) and (b(n)) be increasing and complementary force the equation a(n) = 6 b(n+1) - b(n), with initial value b(0) = 1, to have a unique solution; that is, a pair of complementary sequences (a(n)) = (11,16,21,26,31,...) and (b(n)) = (1,2,3,4,5,6,7,8,9,10,12,...). Conjecture: {a(n) - 6 n} is unbounded below and above.

Links

Table of n, a(n) for n=0..54.

Example

(See A329387.)

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
b = {1}; a = {}; h = 6;
Do[AppendTo[b, mex[Flatten[{a, b}], b[[-1]]]];
AppendTo[a, h b[[-1]] - b[[-2]]], {250}]; a
(* Peter J. C. Moses, Sep 07 2019 *)

Crossrefs

Cf. A329387, A329388, A329390.

Sequence in context: A132990 A074197 A106673 * A227080 A131858 A258588

Adjacent sequences: A329386 A329387 A329388 * A329390 A329391 A329392

Keyword

nonn

Author

Clark Kimberling, Nov 23 2019

Status

approved