OFFSET
0,1
COMMENTS
For n>0, terms with odd indices 3, 13, 59, 569... are much smaller than neighbor terms with even indices.
For n > 0, a(n) >= A053669(n)^(n+1) - n. - Robert Israel, Sep 25 2024
LINKS
Robert Israel, Table of n, a(n) for n = 0..1000
EXAMPLE
2+0=2(prime), 3+1=4=2*2, 43+2=45=3*3*5, 13+3=16=2^4, 239+4=243=3^5,59+5=64=2^6,171869+6=171875=5^6*11,569+7=574=2^6*3^2,
32797+8=32805=3^5*5, 2551+9=2590=2^9*5, 649529+10=649539=3^10*11, 6133+11=6143=2^11*3.
MAPLE
f:= proc(n)
uses priqueue;
local pq, t, v, p, w, i;
initialize(pq);
p:= 2;
while n mod p = 0 do p:= nextprime(p) od;
insert([-p^(n+1), [p$(n+1)]], pq);
do
t:= extract(pq);
v:= -t[1]; w:= t[2];
if isprime(v-n) then return v-n fi;
p:= nextprime(w[-1]);
while n mod p = 0 do p:= nextprime(p) od:
for i from n+1 to 1 by -1 while w[i] = w[n+1] do
insert([t[1]*(p/w[n+1])^(n+2-i), [op(w[1..i-1]), p$(n+2-i)]], pq);
od od
end proc:
f(0):= 2:
map(f, [$0..40]); # Robert Israel, Sep 25 2024
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Zak Seidov, Feb 14 2015
EXTENSIONS
More terms from Robert Israel, Sep 25 2024
STATUS
approved