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Lexicographically earliest sequence of distinct positive integers such that the absolute value of the first difference contains only distinct prime numbers.
2

%I #6 Oct 14 2017 10:46:34

%S 1,3,6,11,4,15,2,19,38,7,30,59,12,49,8,51,104,21,80,9,70,137,10,83,

%T 162,5,94,191,18,119,16,123,14,127,258,17,154,293,22,171,20,183,350,

%U 13,192,373,24,215,408,25,222,23,234,457,26,253,482,33,266,27,278

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

%C This sequence is a variant of A081145 and of A230455.

%C See A293667 for the first difference of this sequence.

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

%H Rémy Sigrist, <a href="/A293666/a293666.gp.txt">PARI program for A293666</a>

%e The following table shows the first terms, alongside the first terms of the first difference:

%e n a(n) a(n+1)-a(n)

%e -- ---- -----------

%e 1 1 2

%e 2 3 3

%e 3 6 5

%e 4 11 -7

%e 5 4 11

%e 6 15 -13

%e 7 2 17

%e 8 19 19

%e 9 38 -31

%e 10 7 23

%e 11 30 29

%e 12 59 -47

%e 13 12 37

%e 14 49 -41

%e 15 8 43

%e 16 51 53

%e 17 104 -83

%e 18 21 59

%e 19 80 -71

%e 20 9 61

%o (PARI) See Links section.

%Y Cf. A081145, A230455, A293667.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Oct 14 2017