A329388 Solution sequence (a(n)) of the complementary equation a(n) = 5 b(n+1) - b(n), with b(0) = 1.

9, 13, 17, 21, 25, 29, 33, 42, 45, 49, 58, 61, 65, 74, 77, 81, 90, 93, 97, 106, 109, 113, 122, 125, 129, 138, 141, 145, 149, 153, 157, 161, 165, 174, 177, 186, 189, 193, 202, 205, 209, 213, 217, 221, 225, 229, 238, 241, 250, 253, 257, 266, 269, 273, 277, 281

Offset

0,1

Comments

The conditions that (a(n)) and (b(n)) be increasing and complementary force the equation a(n) = 5 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)) = (9,13,17,21,25,29,...) and (b(n)) = (1,2,3,4,5,6,7,8,10, ...). Conjecture: {a(n) - 5 n} is unbounded below and above.

Links

Table of n, a(n) for n=0..55.

Example

(See A329387.)

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
b = {1}; a = {}; h = 5;
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, A329389, A329390.

Sequence in context: A186427 A050109 A294357 * A227062 A134441 A174055

Adjacent sequences: A329385 A329386 A329387 * A329389 A329390 A329391

Keyword

nonn

Author

Clark Kimberling, Nov 23 2019

Status

approved