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

1,1

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

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

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

Sequence in context: A320577 A199805 A053248 * A264272 A264257 A111072

Adjacent sequences: A081544 A081545 A081546 * A081548 A081549 A081550

Keyword

nonn

Author

Amarnath Murthy, Apr 01 2003

Extensions

More terms from Vladeta Jovovic, Apr 02 2003

Status

approved