

A297999


Solution (a(n)) of the nearcomplementary equation a(n) = a(1)*b(n)  a(0)*b(n1) + n, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, , b(2) = 5, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.


3



1, 2, 8, 10, 12, 16, 19, 22, 23, 25, 29, 30, 34, 35, 41, 43, 44, 46, 52, 52, 54, 60, 60, 62, 64, 66, 70, 75, 77, 78, 80, 82, 84, 88, 91, 92, 94, 96, 98, 102, 105, 108, 111, 112, 114, 118, 119, 121, 123, 127, 132, 134, 137, 140, 141, 143, 147, 148, 154, 156
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OFFSET

0,2


COMMENTS

The sequence (a(n)) generated by the equation a(n) = a(1)*b(n)  a(0)*b(n1) + n, with initial values as shown, includes duplicates; e.g. a(18) = a(19) = 52. If the duplicates are removed from (a(n)), the resulting sequence and (b(n)) are complementary. Conjectures:
(1) 0 <= a(k)  a(k1) <= 6 for k>=1;
(2) if d is in {0,1,2,3,4,5,6}, then a(k) = a(k1) + d for infinitely many k.
***
See A298000 and A297830 for guides to related sequences.


LINKS

Clark Kimberling, Table of n, a(n) for n = 0..2000


EXAMPLE

a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, b(2) = 5, so that a(2) = 8.
Complement: (b(n)) = (3,4,5,6,7,9,11,13,14,15,17, ...)


MATHEMATICA

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5;
a[n_] := a[1]*b[n]  a[0]*b[n  1] + n;
Table[{a[n], b[n + 1] = mex[Flatten[Map[{a[#], b[#]} &, Range[0, n]]], b[n  0]]}, {n, 2, 3000}];
Table[a[n], {n, 0, 150}] (* A297999 *)
Table[b[n], {n, 0, 150}] (* A298110 *)
(* Peter J. C. Moses, Jan 16 2018 *)


CROSSREFS

Cf. A297997, A298000, A297830, A298110.
Sequence in context: A022298 A229090 A265670 * A287088 A296342 A328559
Adjacent sequences: A297996 A297997 A297998 * A298000 A298001 A298002


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 09 2018


STATUS

approved



