OFFSET
0,1
COMMENTS
Here, nextprime(x) = min { p > x; p prime }, prevprime(x) = max { p < x; p prime }.
The next term, a(10) ~ 3.1*10^196, is too large to be displayed above.
From a(3) on, a(n+1) has roughly twice the number of digits of a(n).
For n >= 1, a(n) is the least prime such that Product_{k=0..n} a(k) is deficient. This implies that (Product_{k=0..n-1} a(k))*prevprime(a(n)) is perfect for n = 1, and a primitive weird number (A002975) for some but not all larger n.
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..13
EXAMPLE
Let Q(x) = 1/(2/sigma[-1](x) - 1), P(n) = Product(a(k), k=0..n-1), and start with a(0) = 4 = P(1). Then:
Q(P(1)) = 7, a(1) = 11. (4*7 is perfect, P(2) = 4*11 is deficient.)
Q(P(2)) = 21, a(2) = 23. (4*11*19 is weird, P(3) = 4*11*23 is deficient.)
Q(P(3)) = 252, a(3) = 257. (P(3)*251 is weird, P(4) = 4*11*23*257 is deficient.)
Q(P(4)) = 13003.2, a(4) = 13007. (P(4)*13003 is weird, P(5) = 4*11*23*257*13007 is deficient.)
Q(P(5)) = 44512006.7..., a(5) = 44512049. (P(5)*44511949 is weird ; P(6) = 4*11*257*44512049 is deficient.)
P(6)*prevprime(a(6)) is semiperfect, i.e., no more weird.
PROG
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
M. F. Hasler, Nov 23 2017
STATUS
approved