A260951 a(1)=1; a(n) is the index of the least primorial (A002110) such that 2*primorial - n-th prime is prime, or -1 if no such primorial exists.

1, -1, 2, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 4, 4, 4, 4, 6, 4, 4, 5, 5, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 7, 5, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 20, 4, 4, 6, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 7, 6, 6, 6, 5, 6, 8, 5, 5, 5, 6, 5, 5, 6, 6, 5, 5, 8, 5, 5, 22, 5, 5, 5, 8, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 11

Offset

1,3

Comments

If Goldbach’s conjecture is true, a(n) > 0 would always exist for n > 2.

Links

Jean-Marc Rebert, Table of n, a(n) for n = 1..10000

Example

a(1)=1, because the first prime is 2, primorial 1# = 2 and 2*2 - 2 = 2 is prime.
a(2) = -1, because the second prime is 3, 2# = 6 and 2*6 - 3 = 9 is not prime.

Prog

(PARI)
a002110(n)=prod(i=1, n, prime(i))
a(n) = my(y=-1); for(k=1, n, if(isprime(2*a002110(k) - prime(n)), y=k; break)); y

Crossrefs

Cf. A002110.

Sequence in context: A002948 A117113 A239430 * A240600 A227183 A162439

Adjacent sequences: A260948 A260949 A260950 * A260952 A260953 A260954

Keyword

sign

Author

Jean-Marc Rebert, Aug 05 2015

Status

approved