

A298002


Solution of the complementary equation a(n) = a(1)*b(n)  a(0)*b(n1) + 4*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, 14, 19, 24, 29, 34, 39, 44, 49, 54, 61, 65, 70, 75, 82, 86, 91, 96, 103, 107, 112, 117, 124, 128, 133, 138, 145, 149, 154, 159, 166, 170, 175, 180, 187, 191, 196, 201, 208, 212, 217, 222, 229, 233, 238, 243, 248, 253, 260, 264, 269, 276, 280, 285, 290
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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 A298000 for a guide to related sequences.
Conjecture: a(n)  n*L < 4 for n >= 1, where L = 3 + sqrt(5).


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, b(2) = 5, so that a(2) = 14.
Complement: (b(n)) = (3,4,5,6,7,8,9,10,11,13,15,17,18,20...)


MATHEMATICA

a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5;
a[n_] := a[n] = a[1]*b[n]  a[0]*b[n  1] + 4 n;
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}] (* A298002 *)


CROSSREFS

Cf. A297800, A297826, A297836, A297837.
Sequence in context: A032476 A274062 A059205 * A217075 A187261 A101398
Adjacent sequences: A297999 A298000 A298001 * A298003 A298004 A298005


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 08 2018


STATUS

approved



