|
|
A242855
|
|
Catalan numbers C(n) such that sum of the factorials of digits of C(n) is prime.
|
|
2
|
|
|
2, 16796, 263747951750360, 1002242216651368, 104088460289122304033498318812080, 22033725021956517463358552614056949950, 1000134600800354781929399250536541864362461089950800, 216489185503133990863274261791925599831188392742851863147080
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The n-th Catalan number C(n) = (2*n)!/(n!*(n+1)!).
The next term, a(9), has 66 digits which is too large to display in data section.
The 102nd term, a(102), having 992 digits, is the last term in b-file.
a(103) has 1021 digits, hence not included in b-file.
|
|
LINKS
|
|
|
EXAMPLE
|
16796 = (2*10)!/(10!*(10+1)!) is 10th Catalan number: 1!+6!+7!+9!+6! = 369361 which is prime.
263747951750360 = (2*28)!/(28!*(28+1)!) is 28th Catalan number: 2!+6!+3!+7!+4!+7!+9!+5!+1!+7!+5!+0!+3!+6!+0! = 379721 which is prime.
|
|
MAPLE
|
with(numtheory):A242855:= proc() if isprime(add( i!, i = convert(((2*n)!/(n!*(n+1)!)), base, 10))((2*n)!/(n!*(n+1)!))) then RETURN ((2*n)!/(n!*(n+1)!)); fi; end: seq(A242855 (), n=1..50);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|