A298469 -id:A298469 - cp's OEIS frontend

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

N. J. A. Sloane, Nov 07 2019

nonn

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].

			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, ...

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

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

A328986 The sequence C(n) defined in the comments (A and B smallest missing numbers, offset 1).

Original entry on oeis.org

4, 10, 16, 21, 28, 33, 39, 45, 51, 57, 62, 68, 74, 80, 86, 91, 98, 103, 109, 115, 120, 127, 132, 138, 144, 150, 156, 161, 168, 173, 179, 185, 190, 197, 202, 208, 214, 220, 226, 231, 237, 243, 249, 255, 260, 267, 272, 278, 284, 290, 296, 301, 307, 313, 319

Offset: 1

N. J. A. Sloane, Nov 07 2019

nonn

Define a triple of sequences A,B,C by A[1]=1, B[1]=2, C[1]=4; for n>=2, 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 = A286660, B = A080652, C = the present sequence.
Inspired by the triples [A003144, A003145, A004146] and [A298468, A298469, A047218].

			The initial terms are:
n: 1, 2, 3, 4,  5,  6,  7,  8.  9. 10. 11, 12, ...
A: 1, 3, 6, 8, 11, 13, 15, 18, 20, 23, 25, 27, ...
B: 2, 5, 7, 9, 12, 14, 17, 19, 22, 24, 26, 29, ...
C: 4, 10, 16, 21, 28, 33, 39, 45, 51, 57, 62, 68, ...

Cf. A286660, A080652; A003144, A003145, A003146; A298468, A298469, A047218.

cp's OEIS Frontend

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

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