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

Author

Clark Kimberling

Keywords

• nonn
• easy

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

Crossrefs

Cf. A022424 and references therein.

Programs

Mathematica

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

Extensions

More terms from Jon E. Schoenfield, Apr 02 2010