A084727 - OEIS

%I #16 Aug 05 2021 12:01:25

%S 2,3,7,281,76561,576577,17873857,643458817,337767408001,

%T 21617114112001,39916801,119715577952256001,1980990543353657472001,

%U 26582634158080001,3577861898239093446857008573440001,711975497511453268455460274177

%N Primes arising in A084726.

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

%C Conjecture: All terms exist.

%C If n! + 1 is prime (A002981) then a(n) = A088332(n). - _Hugo Pfoertner_, Nov 18 2004

%H Nathaniel Johnston, <a href="/A084727/b084727.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = 1 + Product_{i = 0..n-1} (1 + i*A084726(n)). - _David Wasserman_, Jan 03 2005

%e a(1) = 2 = 1 + 1;

%e a(4) = 281 = 1*4*7*10 + 1 (1*2*3*4 + 1 = 25 is composite);

%e a(5) = 76561 = 1*8*15*22*29 + 1.

%p 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

%t 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 *)

%Y Cf. A002981, A084726, A088332.

%K nonn

%O 1,1

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 13 2003

%E More terms from _David Wasserman_, Jan 03 2005