A309252 a(n) is the least number not in the sequence so far and whose absolute difference from a(n-1) is not in the sequence so far, with a(1) = 1 and a(2) = 2.

1, 2, 5, 8, 4, 7, 10, 13, 16, 19, 22, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101

Offset

1,2

Comments

a(n) (mod 3) != 0;

a(n) >= n except for n= 5, 12, 26, 54, 110, 222, 446, 894, ...;

a(n) < 2n except for n= 4, 11, 25, 53, 109, 221, 445, 893, ...;

First occurrence of k or 0 if impossible: 1, 2, 0, 5, 3, 0, 6, 4, 0, 7, 12, 0, 8, 13, 0, 9, 14, 0, 10, 15, 0, 11, 16, 0, 26, 17, 0, 27, 18, 0, ..., .

Links

Table of n, a(n) for n=1..70.

Example

a(3) cannot be 3 since 3-2 = 1 which is a(1), it cannot be 4 since 4-2 = 2 which is a(2), but a(3) can be 5.

Maple

b:= proc(n) option remember; n in {1, 2} end:
a:= proc(n) option remember; local k, t; if n<3 then n
      else t:= a(n-1); for k while b(k) or
           b(abs(k-t)) do od; b(k):= true; k fi
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 19 2019

Mathematica

a[n_] := a[n] = Block[{b = a[n -1], k = 3, s = Array[a, n -1]}, While[ MemberQ[s, k] || MemberQ[s, Abs[b -k]], k++]; k]; a[1] = 1; a[2] = 2; Array[a, 70]

Crossrefs

Cf. A001651, A005408.

Sequence in context: A341488 A114550 A094001 * A020859 A062089 A011201

Adjacent sequences: A309249 A309250 A309251 * A309253 A309254 A309255

Keyword

nonn

Author

Robert G. Wilson v, Jul 18 2019

Status

approved