This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368690 #17 Jan 31 2024 07:58:04 %S A368690 5,2,4,2,8,3,9,6,7,2,8,7,10,6,9,2,7,6,9,6,17,8,16,8,6,5,8,2,3,16,7,15, %T A368690 7,5,9,10,7,6,8,2,15,6,14,6,5,10,8,9,6,5,7,7,16,3,14,5,13,2,14,4,9,7, %U A368690 8,5,5,13,6,6,15,2,13,11,10,12,28,5,13,3,8,6,7,15,3,4,12,5 %N A368690 Number of terms in the trajectory from n to 2 of the map x -> A368241(x), or -1 if n never reaches 2. %C A368690 It is conjectured that every starting n reaches 2 eventually. %C A368690 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 A368690 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. %e A368690 For n=4 the trajectory is 4 -> 6 -> 9 -> 13 -> 2 (row 4 of A368196) which has a(4) = 5 terms. %o A368690 (PARI) f(n) = if (isprime(n), n - precprime(n-1), n + primepi(n)); \\ A368241 %o A368690 a(n) = my(k=1); while ((n = f(n)) != 2, k++); k+1; \\ _Michel Marcus_, Jan 03 2024 %Y A368690 Cf. A368241. %Y A368690 Cf. A000720, A005171, A010051, A006512. %K A368690 nonn %O A368690 4,1 %A A368690 _Hendrik Kuipers_, Jan 03 2024