A136344 Least primes p1 such that gap between p1 and p2=nextprime(p1) contains no semiprimes. Gap is 1 for n=0 (first term) and 2n for n=1..30.

2, 11, 97, 601, 6473, 2521, 35117, 63113, 39343, 104659, 705053, 512821, 1123279, 4357781, 4942711, 4808987, 5922317, 32995057, 105484481, 37212113, 108525829, 335433389, 598559963, 789565537, 864056573, 1913815493, 2311939579

Offset

1,1

Comments

Indices of primes are: 1, 5, 25, 110, 840, 369, 3745, 6329, 4142, 9990, 56934, 42502, 87392, 306589, 344750, 336038, 407897, 2031387, 6058935, 2273894, 6223604, 18062361, 31253527, 40636901, 44264857, 94194169, 112738722, 128926127, 19290534, 258502581, 413356835. Notice that indices (and primes) are not necessarily monotonically increasing. Cf. A133478 (semiprime gaps without primes).

Links

Table of n, a(n) for n=1..27.

Example

a(1)=2 because gap=3-2=1 and between 2 and 3 there is no semiprimes,
a(2)=11 because gap=11-13=2 and between 11 and 13 there is no semiprimes,
a(3)=97 because gap=97-101=4 and between 97 and 101 there is no semiprimes,
a(31)=9042022037 because gap=9042022037-9042022097=60 and between 9042022037 and 9042022097 there is no semiprimes.

Crossrefs

Cf. A133478.

Sequence in context: A227465 A295099 A227466 * A055680 A260957 A368292

Adjacent sequences: A136341 A136342 A136343 * A136345 A136346 A136347

Keyword

nonn

Author

Zak Seidov, Dec 24 2007

Status

approved