A328987 The sequence C(n) defined in the comments (A and B smallest missing numbers, offset 0).

3, 10, 15, 20, 27, 32, 39, 44, 51, 56, 61, 68, 73, 80, 85, 90, 97, 102, 109, 114, 119, 126, 131, 138, 143, 150, 155, 160, 167, 172, 179, 184, 189, 196, 201, 208, 213, 220, 225, 230, 237, 242, 249, 254, 259, 266, 271, 278, 283, 290, 295, 300, 307, 312, 319

Offset

0,1

Comments

Define a triple of sequences A,B,C by A[0]=1, B[0]=2, C[0]=3; for n>=1, A[n] = smallest missing number from the terms of A,B,C defined so far; B[n] = = smallest missing number from the terms of A,B,C defined so far; C[n] = n+A[n]+B[n].

Then A = A086377, B = A080652, C = the present sequence.

Inspired by the triples [A003144, A003145, A004146] and [A298468, A298469, A047218].

Links

Table of n, a(n) for n=0..54.

Formula

Conjectures from Colin Barker, Nov 08 2019: (Start)

G.f.: (3 + 7*x + 5*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 7*x^6 + 5*x^7 + 7*x^8 + 5*x^9 + 5*x^10 + 7*x^11 + 2*x^12 - 2*x^20 + 2*x^21) / (1 - x - x^12 + x^13).

a(n) = a(n-1) + a(n-12) - a(n-13) for n>21.

(End)

Conjecture: a(n) ~ 35*n/6. - Stefano Spezia, Nov 02 2021

Example

The initial terms are:
n: 0, 1, 2, 3, 4,  5,  6,  7,  8.  9. 10. ...
a: 1, 4, 6, 8, 11, 13, 16, 18, 21, 23,25, ...
b: 2, 5, 7, 9, 12, 14, 17, 19, 22, 24,26, ...
c: 3, 10, 15, 20, 27, 32, 39, 44, 51, 56, 61, 68, 73, ...

Crossrefs

Cf. A086377, A080652; A003144, A003145, A003146; A298468, A298469, A047218.

Sequence in context: A141463 A134102 A173600 * A108770 A112355 A074314

Adjacent sequences: A328984 A328985 A328986 * A328988 A328989 A328990

Keyword

nonn

Author

N. J. A. Sloane, Nov 07 2019

Status

approved