A145173 Least a(n) such that p(n)#*(p(n)# - a(n)) - 1 is prime, where p(i)# is the i-th primorial.

0, 1, 2, 1, 2, 4, 2, 1, 4, 9, 1, 2, 14, 2, 3, 9, 2, 9, 24, 1, 25, 1, 7, 8, 2, 52, 14, 13, 42, 7, 22, 8, 5, 20, 36, 9, 8, 10, 36, 56, 2, 14, 42, 7, 2, 128, 159, 45, 49, 1, 16, 69, 211, 80, 19, 13, 3, 12, 25, 21, 106, 32, 39, 26, 21, 23, 5, 22, 66, 43, 45, 139, 350, 38, 26, 145, 19, 142

Offset

1,3

Comments

As n increases, Sum_{i=1..n} a(n) tends to n*(n+1)/2.

Links

Pierre CAMI, Table of n, a(n) for n = 1..704

Example

2*(2-0) - 1 = 3, which is prime, so a(1)=0;
2*3*(2*3 - 1) - 1 = 29, which is prime, so a(2)=1;
2*3*5*(2*3*5 - 2) - 1 = 839, which is prime, so a(3)=2.

Prog

(PARI) { allocatemem(932245000); default(primelimit, 4294965247); n=0; p=1; q=1; until (0, n=n+1; p=nextprime(p+1); q=q*p; for (a=0, 1000000000, r=q*(q-a)-1; if (isprime(r), print(n, " ", a); write("b145173.txt", n, " ", a); break; ); ) ) } \\ Harry J. Smith, Jan 14 2009

Crossrefs

Cf. A144946, A144947.

Sequence in context: A097082 A281729 A302290 * A361656 A270594 A270706

Adjacent sequences: A145170 A145171 A145172 * A145174 A145175 A145176

Keyword

nonn

Author

Pierre CAMI, Oct 03 2008

Extensions

Corrected by several correspondents, Jan 14 2009

Status

approved