A325417 a(n) is the least number not 2*a(m) or 3*a(m)+1 for any m < n.

1, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19, 20, 21, 23, 27, 29, 31, 32, 33, 35, 36, 39, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 55, 56, 57, 59, 60, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 99, 101, 103, 104

Offset: 1

Author

Clark Kimberling, Apr 24 2019

Keywords

• nonn
• easy

Comments

In column 1 of the following guide to related sequences, disallowed terms are indicated by the variable x representing a(m) for m < n.

Disallowed Sequence(a) Complement(c) Differences(a) Differences(c)

2x, 3x+1 A325417 A325418 A325444 A325445

3x, 2x+1 A325419 A325420 A325494 A325495

2x+1, 3x+1 A077477 A325422 A325496 A325497

2x, 3x A036668 A325424 A325498 A325499

[3x/2], 2x A325425 A325426 A325518 A325519

[3x/2], 2x+1 A325427 A325428 A325520 A325521

[3x/2], 3x A325429 A325430 A325522 A325523

3x, 4x A325431 A325432 A325525 A325526

2x, 3x-1 A325462 A325463 A325526 A325527

2x, 3x-2 A325464 A325465 A325528 A325529

2x-1, 3x-1 A325440 A325441 A325530 A325531

2x-1, 3x A325442 A325443 A325532 A325533

2x+1, 3x+2 A325539 A325540 A325541 A325542

Examples

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the numbers 2 and 4 are disallowed, so that a(2) = 3, whence the numbers 6 and 10 are disallowed, so that a(3) = 5.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A325418, A325444.

Programs

Mathematica

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
IntegerQ]]] &]], {150}]; a     (* A325417 *)
Complement[Range[Last[a]], a]  (* A325418 *)
(* Peter J. C. Moses, Apr 23 2019 *)