OFFSET
1,1
COMMENTS
For prime p in this sequence, b(p) = r*b(p-r) where b(m) = A288814(m), and r = gpf(b(p)) is some prime < q. We can say that prime p_n (n > 2) is of type k if gpf(b(p_n)) = p_(n-k).
LINKS
David A. Corneth, Table of n, a(n) for n = 1..31763 (terms up to 5*10^6; first 544 terms from Robert Israel)
David A. Corneth, PARI program.
EXAMPLE
p=211 is a candidate for inclusion because p-q = 211-199 = 12, and b(12)=35 is a term in A292081. Since r=197 is the next prime below q, p-r = 14 and b(14) = 33 < 35, 211 is in the sequence, of type 2.
Conversely, p=809, which also has gap p-q = 12, is not in the sequence because the only number n > 12 for which b(n) < b(12)=35 is n=14, and p-14 = 795 is not prime. Therefore b(809) = 797*b(12) = 27895, and 809 is of type 1.
MAPLE
N:= 10^7: # to get terms before the first prime p>3 such that A288814(p) > N
Res:= NULL:
for x from 4 to N do
if isprime(x) then next fi;
F:= ifactors(x)[2];
p:= add(t[1]*t[2], t=F);
if not isprime(p) then next fi;
if not assigned(A288814[p]) then
A288814[p]:= x;
w:= max(seq(t[1], t=F));
if w < prevprime(p) then
Res:= Res, p
fi
fi
od:
pmax:= Res[-1]:
Primes:= select(isprime, [seq(i, i=5..pmax, 2)]):
B:= remove(p -> assigned(A288814[p]), Primes):
sort(select(`<`, [Res], min(B))); # Robert Israel, Oct 19 2017
PROG
(PARI) \\ See PARI link. - David A. Corneth, Mar 23 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David James Sycamore, Sep 13 2017
EXTENSIONS
a(30)-a(50) from Robert Israel, Oct 02 2017
Edited by Michel Marcus, Nov 15 2023
STATUS
approved