

A297833


Solution of the complementary equation a(n) = a(1)*b(n1)  a(0)*b(n2) + 2*n  3, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.


3



1, 2, 6, 9, 14, 16, 21, 23, 26, 29, 34, 38, 40, 43, 46, 51, 55, 57, 62, 64, 69, 71, 74, 77, 82, 84, 87, 92, 96, 98, 103, 105, 110, 112, 115, 118, 123, 125, 128, 133, 137, 139, 142, 145, 150, 154, 156, 159, 162, 167, 171, 173, 178, 180, 185, 187, 190, 193
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OFFSET

0,2


COMMENTS

The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A297830 for a guide to related sequences.
Conjecture: 2 < a(n)  (2 +sqrt(2))*n <= 1 for n >= 1.


LINKS



EXAMPLE

a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, so that a(2) = 6.
Complement: (b(n)) = (3,4,5,7,8,10,12,13,15,17,18,19,...)


MATHEMATICA

a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = a[1]*b[n  1]  a[0]*b[n  2] + 2 n  3;
j = 1; While[j < 100, k = a[j]  j  1;
While[k < a[j + 1]  j + 1, b[k] = j + k + 2; k++]; j++]; k
Table[a[n], {n, 0, k}] (* A297833 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



