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A297834 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 4, 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, 5, 8, 12, 17, 19, 22, 27, 29, 32, 35, 40, 44, 46, 51, 53, 56, 59, 64, 68, 70, 75, 77, 82, 84, 87, 90, 95, 97, 100, 105, 109, 111, 114, 117, 122, 126, 128, 133, 135, 140, 142, 145, 148, 153, 155, 158, 163, 167, 169, 172, 175, 180, 184, 186, 189, 192 (list; graph; refs; listen; history; text; internal format)
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: -3 < a(n) - (2 +sqrt(2))*n <= 1 for n >= 1.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..10000

EXAMPLE

a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, so that a(2) = 5.

Complement: (b(n)) = (3,4,6,7,9,10,11,13,14,15,16,18,20,...)

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 - 4;

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}]  (* A297834 *)

CROSSREFS

Cf. A297826, A297830.

Sequence in context: A174605 A108577 A272719 * A036789 A330188 A214047

Adjacent sequences:  A297831 A297832 A297833 * A297835 A297836 A297837

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 04 2018

STATUS

approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)