A128824 First prime which is 2k greater than the product of lesser twin primes.

5, 7, 11, 13, 17, 19, 23, 37, 29, 31, 47, 37, 41, 43, 47, 61, 53, 67, 59, 61, 227, 67, 71, 73, 89, 79, 83, 97, 89, 103, 107, 97, 101, 103

Offset

1,1

Comments

In the example, 37 is the only number possible for 2k=22. Twinl#(1)= 3 and 3+22 = 25, not prime. Twinl#(n), n>2, is a multiple of 11 so adding 22 will always result in a multiple of 11 and not prime. If k is a multiple of a lesser twin prime, then the number of primes in twinl#(n)+2k is finite.

Links

Table of n, a(n) for n=1..34.

Formula

Define twinl#(n)as the product of the first n lesser twin primes. Then if twinl#+2k k=1,2,3... is prime, list it.

Example

Twinl#(2) + 2*11 = 37, the first prime 22 greater than twinl#(2).

Prog

(PARI) twiprimesl(n, a) = { local(pr, x, y, j); for(j=1, n, pr=1; for(x=1, j, pr*=twinl(x); ); y=pr+a; if(ispseudoprime(y), print1(y", ") ) ) } twinl(n) = \The n-th lower twin prime { local(c, x); c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++; ); return(prime(x-1)) }

Crossrefs

Sequence in context: A118941 A096547 A216524 * A098420 A346676 A309726

Adjacent sequences: A128821 A128822 A128823 * A128825 A128826 A128827

Keyword

nonn

Author

Cino Hilliard, May 08 2007

Status

approved