A081547 Smallest composite number which is 1 more than the product of n (not necessarily distinct) prime numbers.

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

Author

Amarnath Murthy, Apr 01 2003

Keywords

• nonn

Comments

a(2*n+1) = 2^(2*n+1)+1, n>0. - Vladeta Jovovic, Apr 02 2003

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A081545, A081546, A081548, A073919, A007583.

Programs

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 *)

Python

from sympy import isprime
def A081547(n): return 10 if n==2 else ((3<Chai Wah Wu, Sep 02 2024

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

Extensions

More terms from Vladeta Jovovic, Apr 02 2003