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A329388 Solution sequence (a(n)) of the complementary equation a(n) = 5 b(n+1) - b(n), with b(0) = 1. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 4 12:18 EDT 2020. Contains 335448 sequences. (Running on oeis4.)