A293666 Lexicographically earliest sequence of distinct positive integers such that the absolute value of the first difference contains only distinct prime numbers.

1, 3, 6, 11, 4, 15, 2, 19, 38, 7, 30, 59, 12, 49, 8, 51, 104, 21, 80, 9, 70, 137, 10, 83, 162, 5, 94, 191, 18, 119, 16, 123, 14, 127, 258, 17, 154, 293, 22, 171, 20, 183, 350, 13, 192, 373, 24, 215, 408, 25, 222, 23, 234, 457, 26, 253, 482, 33, 266, 27, 278

Offset: 1

Author

Rémy Sigrist, Oct 14 2017

Keywords

• nonn

Comments

This sequence is a variant of A081145 and of A230455.

See A293667 for the first difference of this sequence.

For n > 1, n is even iff a(n) is odd.

Examples

			The following table shows the first terms, alongside the first terms of the first difference:
n       a(n)    a(n+1)-a(n)
--      ----    -----------
1       1       2
2       3       3
3       6       5
4       11      -7
5       4       11
6       15      -13
7       2       17
8       19      19
9       38      -31
10      7       23
11      30      29
12      59      -47
13      12      37
14      49      -41
15      8       43
16      51      53
17      104     -83
18      21      59
19      80      -71
20      9       61
		

Links

• Rémy Sigrist, PARI program for A293666

Crossrefs

Cf. A081145, A230455, A293667.

Programs

PARI

See Links section.