A352171 - OEIS

%I #6 Mar 13 2022 19:09:59

%S 7,13,3,1547803

%N a(n) is the start of a sequence of exactly n members of A023200 under the iteration p -> 3*p+4.

%C Let s(1) = a(n) and s(k+1) = 3*s(k)+4.  Then s(1), ..., s(n) are in A023200 but s(n+1) is not in A023200, and a(n) is the least value of s(n) for which this is the case.

%e a(3) = 3 because with s(1) = 3 we have s(2) = 3*3+4 = 13, s(3) = 3*13+4 = 43, s(4) = 3*43+4 = 133; 3, 13, and 43 are in A023200 because 3, 7, 13, 17, 42, 47 are prime, but 133 is not in A023200 because 133 is composite.

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

%p   if isprime(p) and isprime(p+4) then 1 + procname(3*p+4) else 0 fi

%p end proc:

%p V:= Vector(5): V[1]:= 7: V[3]:= 3: count:= 2:

%p for p from 13 by 30 while count < 5 do

%p v:= f(p);

%p if v > 0 and V[v] = 0 then count:= count+1; V[v]:= p; fi

%p od:

%p convert(V,list);

%Y Cf. A023200.

%K nonn,more

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Mar 07 2022