A288798 - OEIS

%I #5 Jun 16 2017 22:22:09

%S 1,2311,4621,331,2641,4951,121,2431,4741,451,2761,31,2341,4651,361,

%T 2671,4981,151,2461,4771,481,2791,61,2371,4681,391,2701,5011,181,2491,

%U 4801,511,2821,91,2401,4711,421,2731,5041,211,2521,4831,541,2851,5161,871,3181

%N Lexicographically earliest sequence of distinct positive terms such that the absolute difference of two consecutive terms has at least 5 distinct prime factors.

%C Conjecturally: this sequence is a permutation of the natural numbers, and a(n) ~ n.

%C This sequence is related to A280659: here we consider the absolute difference, there the sum, of consecutive terms.

%H Rémy Sigrist, <a href="/A288798/b288798.txt">Table of n, a(n) for n = 1..25000</a>

%H Rémy Sigrist, <a href="/A288798/a288798.gp.txt">PARI program for A288798</a>

%e The first terms, alongside the primes p dividing |a(n) - a(n+1)|, are:

%e n       a(n)    p

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

%e 1       1       2, 3, 5, 7, 11

%e 2       2311    2, 3, 5, 7, 11

%e 3       4621    2, 3, 5,    11, 13

%e 4       331     2, 3, 5, 7, 11

%e 5       2641    2, 3, 5, 7, 11

%e 6       4951    2, 3, 5, 7,         23

%e 7       121     2, 3, 5, 7, 11

%e 8       2431    2, 3, 5, 7, 11

%e 9       4741    2, 3, 5,    11, 13

%e 10      451     2, 3, 5, 7, 11

%e 11      2761    2, 3, 5, 7,     13

%e 12      31      2, 3, 5, 7, 11

%e 13      2341    2, 3, 5, 7, 11

%e 14      4651    2, 3, 5,    11, 13

%e 15      361     2, 3, 5, 7, 11

%e 16      2671    2, 3, 5, 7, 11

%e 17      4981    2, 3, 5, 7,         23

%e 18      151     2, 3, 5, 7, 11

%e 19      2461    2, 3, 5, 7, 11

%e 20      4771    2, 3, 5,    11, 13

%Y Cf. A280659.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jun 16 2017