

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
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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



