A022440 a(n) = c(n-1) + c(n-3) where c is the sequence of positive numbers not in a.

3, 4, 5, 7, 10, 15, 19, 21, 24, 26, 29, 31, 34, 37, 40, 43, 47, 50, 53, 57, 60, 63, 67, 69, 73, 75, 79, 81, 85, 87, 90, 93, 95, 99, 101, 105, 107, 110, 113, 115, 119, 121, 125, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175, 179, 181

Offset

1,1

Comments

From N. J. A. Sloane, Nov 24 2004: I'm not sure of the minimal hypotheses needed to generate this sequence, but one method that works is the following:

Start with a(1)=3, a(2)=4, a(3)=5, so that we know c(1)=1 and c(2)=2. Let c(3) = x >= 6, so that a(4) = 1+x >= 6 and x=6 is forced, with a(4)=7. Then c(4) >= 8, a(5) >= 10, so definitely c(4)=8 and c(5)=9. From now on the sequence extends easily.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Mathematica

Fold[Append[#1, Plus @@ Complement[Range[Max@#1 + 3], #1][[{#2, #2 + 2}]]] &, {3, 4, 5}, Range[59]] (* Ivan Neretin, Mar 30 2017 *)

Crossrefs

Cf. A022424 and references therein.

Sequence in context: A309916 A162311 A003312 * A347805 A088130 A046840

Adjacent sequences: A022437 A022438 A022439 * A022441 A022442 A022443

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Jon E. Schoenfield, Apr 02 2010

Status

approved