A352171 a(n) is the start of a sequence of exactly n members of A023200 under the iteration p -> 3*p+4.

7, 13, 3, 1547803

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 07 2022

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A023200.

Programs

Maple

f:= proc(p) option remember;
  if isprime(p) and isprime(p+4) then 1 + procname(3*p+4) else 0 fi
end proc:
V:= Vector(5): V[1]:= 7: V[3]:= 3: count:= 2:
for p from 13 by 30 while count < 5 do
v:= f(p);
if v > 0 and V[v] = 0 then count:= count+1; V[v]:= p; fi
od:
convert(V,list);