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

1,1

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

Links

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

Example

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.

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]

Prog

(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);
}

Crossrefs

Sequence in context: A154587 A083020 A033503 * A057206 A057713 A124987

Adjacent sequences: A181613 A181614 A181615 * A181617 A181618 A181619

Keyword

nonn

Author

Bill McEachen, Jan 30 2011

Status

approved