cp's OEIS Frontend

A368196 Irregular triangle read by rows where row n is the trajectory starting from n and ending with 2 of the map x -> A368241(x).

%I A368196 #48 Jan 31 2024 07:58:12
%S A368196 4,6,9,13,2,5,2,6,9,13,2,7,2,8,12,17,4,6,9,13,2,9,13,2,10,14,20,28,37,
%T A368196 6,9,13,2,11,4,6,9,13,2,12,17,4,6,9,13,2,13,2,14,20,28,37,6,9,13,2,15,
%U A368196 21,29,6,9,13,2,16,22,30,40,52,67,6,9,13,2,17,4,6,9,13,2
%N A368196 Irregular triangle read by rows where row n is the trajectory starting from n and ending with 2 of the map x -> A368241(x).
%C A368196 It is conjectured that every starting n reaches 2 eventually. (If not then the sequence has an infinite final row.)
%C A368196 Map A368241(x) decreases to the prime gap x-prevprime(x) when x is prime, or increases to x+primepi(x) otherwise, and will reach 2 when x is the greater of a twin prime pair (A006512, preceding prime gap 2).
%C A368196 Prime gaps and x+primepi(x) may become large, but if the twin prime conjecture is true then there would be large twin primes they might reach too.
%F A368196 T(n,0) = n.
%F A368196 T(n,k) = A368241(T(n,k-1)) for k >= 1.
%e A368196 Table T(n,k) begins:
%e A368196   n\k    0   1   2   3   4   5   6   7   8   9
%e A368196   --------------------------------------------
%e A368196    4:    4   6   9  13   2
%e A368196    5:    5   2
%e A368196    6:    6   9  13   2
%e A368196    7:    7   2
%e A368196    8:    8  12  17   4   6   9  13   2
%e A368196    9:    9  13   2
%e A368196   10:   10  14  20  28  37   6   9  13   2
%e A368196   11:   11   4   6   9  13   2
%e A368196   12:   12  17   4   6   9  13   2
%e A368196   13:   13   2
%e A368196   14:   14  20  28  37   6   9  13   2
%e A368196   15:   15  21  29   6   9  13   2
%e A368196   16:   16  22  30  40  52  67   6   9  13   2
%e A368196   17:   17   4   6   9  13   2
%e A368196   18:   18  25  34  45  59   6   9  13   2
%e A368196   19:   19   2
%e A368196   20:   20  28  37   6   9  13   2
%o A368196 (PARI) row(n) = my(list=List(n)); while(n!=2, n = if (isprime(n), n - precprime(n-1), n + primepi(n)); listput(list, n)); Vec(list); \\ _Michel Marcus_, Dec 17 2023
%Y A368196 Cf. A368241.
%Y A368196 Cf. A000720, A005171, A010051, A006512.
%K A368196 nonn,tabf
%O A368196 4,1
%A A368196 _Hendrik Kuipers_, Dec 16 2023