A084727 Primes arising in A084726.

2, 3, 7, 281, 76561, 576577, 17873857, 643458817, 337767408001, 21617114112001, 39916801, 119715577952256001, 1980990543353657472001, 26582634158080001, 3577861898239093446857008573440001, 711975497511453268455460274177

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 13 2003

Keywords

• nonn

Comments

Smallest prime of the form: 1 + product of n terms of an arithmetic progression with first term 1.

Conjecture: All terms exist.

If n! + 1 is prime (A002981) then a(n) = A088332(n). - Hugo Pfoertner, Nov 18 2004

Examples

			a(1) = 2 = 1 + 1;
a(4) = 281 = 1*4*7*10 + 1 (1*2*3*4 + 1 = 25 is composite);
a(5) = 76561 = 1*8*15*22*29 + 1.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A002981, A084726, A088332.

Programs

Maple

A084727 := proc(n) local k,p: for k from 1 do p:=1+mul(1+j*k,j=0..n-1): if(isprime(p))then return p: fi: od: end: seq(A084727(n),n=1..16); # Nathaniel Johnston, Jun 26 2011

Mathematica

np[n_]:=Module[{k=1},While[!PrimeQ[Times@@NestList[k+#&,1,n-1]+1],k++];Times@@NestList[k+#&,1,n-1]+1]; Array[np,20] (* Harvey P. Dale, Aug 05 2021 *)

Formula

a(n) = 1 + Product_{i = 0..n-1} (1 + i*A084726(n)). - David Wasserman, Jan 03 2005

Extensions

More terms from David Wasserman, Jan 03 2005