A181616 a(1)=5; thereafter a(2n) = nextprime(a(2n-1)^2), a(2n+1) = nextprime(floor(2*a(2n)/(a(2n-1) + 1))) where nextprime(.) is A007918(.).

5, 29, 11, 127, 23, 541, 47, 2213, 97, 9413, 193, 37253, 389, 151337, 787, 619373, 1579, 2493259, 3163, 10004573, 6329, 40056253, 12659, 160250297, 25321, 641153069, 50647, 2565118639, 101293, 10260271859, 202591, 41043113401, 405199

Offset: 1

Author

Bill McEachen, Jan 30 2011

Keywords

• nonn

Comments

This gives a sawtooth log plot a bit reminiscent of Goldbach's comet, with wave frequency and amplitude increasing indefinitely. I started at 5 for no particular reason.

The two "lines" in the graph approach ratio 2.0 and 4.0 respectively for consecutive terms. The two are then (5, 11, 23, 47, ...) and (29, 127, 541, 2213, ...). - Bill McEachen, Sep 27 2013

Examples

			Beginning at 5 (n=1), a(2) via nextprime(5^2) = 29.
Divisor = ceiling(5/2) = 3 so a(3) = nextprime(floor(29/3)) = 11.
Then repeat: a(4) via nextprime(11^2) = 127.
Divisor = ceiling(11/2) = 6 so a(5) = nextprime(floor(127/6)) = 23.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Programs

Maple

A007491 := proc(n) nextprime(n^2) ; end proc:
A181616 := proc(n) option remember; if n = 1 then 5; elif type(n,'even') then A007491(procname(n-1)) ; else 2*procname(n-1)/(procname(n-2)+1) ; nextprime(floor(%)) ; end if; end proc: # R. J. Mathar, Feb 09 2011

Mathematica

a[1] = 5; a[n_] := a[n] = If[OddQ@ n, NextPrime[ a[n - 1]/Ceiling[ a[n - 2]/2]], NextPrime[ a[n - 1]^2]]; Array[a, 33]

PARI

\\ example call newseq9(2,50) to use square power, 1st 50 terms
\\  I never tried any power but 2
newseq9(a,iend)=
{
a=floor(a);
if(a<2,a=2);
i5=5;
print(i5);
for(n=1,iend,
  i6=nextprime(i5^a);
  b=ceil(i5/2);   \\ vary as f{i5}
  i7=nextprime(floor(i6/b));
  print(i6);
  print(i7);
  i5=i7
);  \\end FOR
print("Designed pgm exit (a,b) ...",a," , ",b);
}