|
|
A253633
|
|
a(n) is the least positive integer b such that b^(2^n) + (b-1)^(2^n) is prime.
|
|
4
|
|
|
2, 2, 2, 2, 2, 9, 96, 32, 86, 60, 1079, 755, 312, 3509, 1829, 49958, 22845
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
When a(n) is 2, the corresponding prime is a Fermat prime, otherwise it is a so-called extended generalized Fermat prime sometimes denoted xGF(n, b, b-1) or similar.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
For n = 5, 2^5 = 32 is the exponent. The numbers 1^32 + 0^32, 2^32 + 1^32, ..., 8^32 + 7^32 are not prime, but 9^32 + 8^32 is prime, so a(5) = 9. - Michael B. Porter, Mar 28 2018
|
|
PROG
|
(PARI) a(n)=for(b=2, 10^10, if(ispseudoprime(b^(2^n)+(b-1)^(2^n)), return(b)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|