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A081547
Smallest composite number which is 1 more than the product of n (not necessarily distinct) prime numbers.
2
4, 10, 9, 25, 33, 65, 129, 385, 513, 1025, 2049, 4097, 8193, 16385, 32769, 98305, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649
OFFSET
1,1
COMMENTS
a(2*n+1) = 2^(2*n+1)+1, n>0. - Vladeta Jovovic, Apr 02 2003
LINKS
FORMULA
For n>2, a(n) = 2^n+1 unless this is a Fermat prime (A019434), in which case a(n) = 2^(n-1)*3+1 (which is divisible by 5). - Dean Hickerson, Apr 05 2003
MATHEMATICA
cno[n_]:=Module[{a=2^n+1}, If[PrimeQ[a], 2^(n-1)*3+1, a]]; Join[{4, 10}, Array[cno, 30, 3]] (* Harvey P. Dale, Mar 24 2012 *)
PROG
(Python)
from sympy import isprime
def A081547(n): return 10 if n==2 else ((3<<n-1)+1 if isprime(m:=(1<<n)+1) else m) # Chai Wah Wu, Sep 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 01 2003
EXTENSIONS
More terms from Vladeta Jovovic, Apr 02 2003
STATUS
approved