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A297998 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + floor(5*n/2), 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. 2
1, 2, 10, 13, 17, 20, 24, 27, 33, 35, 41, 43, 47, 52, 55, 60, 63, 66, 72, 74, 80, 82, 86, 89, 93, 98, 103, 105, 109, 112, 116, 121, 126, 128, 132, 137, 140, 143, 147, 152, 155, 160, 163, 166, 170, 175, 178, 183, 186, 191, 194, 197, 201, 204, 210, 214, 217 (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.

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) = 10.

Complement: (b(n)) = (3,4,5,6,7,8,9,11,12,14,15,16,18,19,21,...)

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] + Floor[5/2];

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}]  (* A297998 *)

CROSSREFS

Cf. A297826, A297830, A297836.

Sequence in context: A297835 A298000 A058216 * A037386 A250187 A062317

Adjacent sequences:  A297995 A297996 A297997 * A297999 A298000 A298001

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 04 2018

STATUS

approved

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)