A080841 Number of pairs (p,q) of (not necessarily consecutive) primes with q-p = 6 and q < 10^n.

0, 15, 74, 411, 2447, 16386, 117207, 879908, 6849047, 54818296, 448725003, 3741217498

Offset

1,2

Comments

Note that one has to be careful to distinguish between pairs of consecutive primes (p,q) with q-p = 6 (A031924), and pairs of primes (p,q) with q-p = 6 (A023201). Here we consider the latter, whereas A093738 considers the former. - N. J. A. Sloane, Mar 07 2021

Links

Table of n, a(n) for n=1..12.

A. Granville, G. Martin, Prime number races, Amer. Math. Monthly vol 113, no 1 (2006) p 1.

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].

Prog

(PARI) {c=0; p=7; for(n=1, 9, while(p<10^n, if(isprime(p-6), c++); p=nextprime(p+1)); print1(c, ", "))}

Crossrefs

Cf. A023201, A046117, A007508, A080840, A006512, A046132, A046117.

See also A031924, A093738.

Sequence in context: A212092 A022817 A171341 * A022675 A214453 A317657

Adjacent sequences: A080838 A080839 A080840 * A080842 A080843 A080844

Keyword

nonn

Author

Jason Earls, Mar 28 2003

Extensions

a(8) and a(9) from Klaus Brockhaus, Mar 30 2003

More terms from R. J. Mathar, Aug 05 2007

Status

approved