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A328987 The sequence C(n) defined in the comments (A and B smallest missing numbers, offset 0). 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 (list; graph; refs; listen; history; text; internal format)
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)

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. A286660, 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

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Last modified October 1 04:06 EDT 2020. Contains 337441 sequences. (Running on oeis4.)