A128841 First occurrence of primes that are 2^k greater than the product of lesser twin primes.

5, 7, 11, 19, 47, 67, 131, 271, 677, 1039, 2063, 4099, 3343337, 97729, 32771, 65539, 133877, 262147, 524453, 13971970981, 2097317, 4194319, 8388623, 16777381, 36889577, 67108879, 134217893, 268435459, 536952257, 1073741827, 2147483813

Offset

1,1

Comments

It is interesting from the example that the first three primes 19,31 and 181 greater than twinl#(n) + 2^4 are all greater twin primes. The next prime is the 1824 digit number twinl#(469) + 2^4 and is not part of a twin prime pair.

Links

Table of n, a(n) for n=1..31.

Formula

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

Example

for k=4,Twinl#(1) + 2^4 = 19, the first prime (2^4)-th greater than twinl#(1).

Prog

(PARI) twiprimesl2(n, a) = { local(pr, x, y, j); for(a=0, n, for(j=1, n, pr=1; for(x=1, j, pr*=twinl(x); ); y=pr+2^a; if(ispseudoprime(y), print1(y", "); break ) ) ) } 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: A038881 A190359 A045441 * A057733 A318078 A174332

Adjacent sequences: A128838 A128839 A128840 * A128842 A128843 A128844

Keyword

nonn

Author

Cino Hilliard, May 08 2007

Status

approved