The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A351051 a(n) is the least prime that begins a sequence of exactly n primes under iteration of the map x -> (x^2+2)/3. 0

%I #13 Feb 02 2022 15:08:44

%S 3,11,17,7,25781659,13505561767

%N a(n) is the least prime that begins a sequence of exactly n primes under iteration of the map x -> (x^2+2)/3.

%e 7 is prime, (7^2+2)/3 = 17 is prime, (17^2+2)/3 = 97 is prime, (97^2+2)/3 = 3137 is prime, but (3137^2+2)/3 = 3280257 is not prime, so 7 begins the sequence of 4 primes (7, 17, 97, 3137). Since this is the first prime to do so, a(4) = 7.

%p f:= proc(p) option remember; local q;

%p q:= (p^2+2)/3;

%p if isprime(q) then 1 + procname(q) else 1 fi

%p end proc:

%p A:= Vector(5): count:= 0:

%p p:= 3:

%p while count < 5 do

%p p:= nextprime(p);

%p v:= f(p);

%p if A[v] = 0 then A[v]:= p; count:= count+1; fi;

%p od:

%p convert(A,list);

%t f[n_] := -1 + Length @ NestWhileList[(#^2 + 2)/3 &, n, PrimeQ]; a[n_] := Module[{p = 3}, While[f[p] != n, p = NextPrime[p]]; p]; Array[a, 4] (* _Amiram Eldar_, Feb 01 2022 *)

%Y Cf. A109953.

%K nonn,more

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 30 2022

%E a(6) from _Amiram Eldar_, Feb 01 2022

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 2 23:30 EDT 2023. Contains 365841 sequences. (Running on oeis4.)