A263925 - OEIS

%I #22 Nov 28 2015 19:33:11

%S 3,5,11,19,89,323,29,61,79,199,563,181,353,1307,257,709,1237,1277,

%T 1609,1237,4157,2017,577,157,191,1063,239,823,1607,4159,139,11527,

%U 2339,18457,4079,463,1861,1123,8699,16561,719,4327,9311,1693,3067,4243,22397,4079,3989,24071

%N a(n) = least m > 1 such that m + (prime(n)#)^n is prime.

%C Here prime(n)# denotes the primorial A002110(n), i.e., the product of the first n primes. Terms a(n) are often (but not always) prime; out of the first fifty terms, only one (a(6)=323) is composite.

%C The definition is similar to Fortunate numbers (A005235); however, in A005235 the primorial is not raised to the n-th power. Unlike this sequence, all known Fortunate numbers are prime.

%e (prime(2)#)^2=36. a(2)=5 because 5 is the minimal m>1 such that m+36 is prime.

%t Table[m = 2; While[! PrimeQ[m + Product[Prime@ i, {i, n}]^n], m++]; m, {n, 30}] (* _Michael De Vlieger_, Nov 11 2015 *)

%o (PARI) a(n)=my(s=prod(i=1,n,prime(i))^n); nextprime(s+2)-s

%Y Cf. A002110, A005235, A181555, A264050.

%K nonn,more

%O 1,1

%A _Alexei Kourbatov_, Oct 30 2015