A061351 Between p and the next prime either there are no numbers or there is a single squarefree number.

2, 5, 29, 41, 101, 137, 281, 461, 569, 617, 641, 821, 857, 1229, 1289, 1301, 1481, 1697, 1721, 1877, 2081, 2129, 2237, 2309, 2381, 2657, 2729, 2801, 3389, 3461, 3557, 3917, 3929, 4001, 4217, 4241, 4421, 4637, 4721, 5009, 5441, 5477, 5501, 5657, 6089

Offset

0,1

Comments

Apart from the initial 2, the lesser of twin primes {p, p+2} such that the middle term p+1 is squarefree: intersection[{A014574(n)},{A005117(n)}].

Links

Harry J. Smith, Table of n, a(n) for n=0,...,1000

Example

Between 29 and 31 the only composite is 30, a squarefree number. If next(p)-p>2, a nonsquarefree integer always arises between them.

Prog

(PARI) { n=0; p=3; f="b061351.txt"; write(f, "0 2"); forprime (q=5, 355723, if (q-p == 2, if (issquarefree(p+1), write(f, n++, " ", p))); p=q ) } \\ Harry J. Smith, Jul 21 2009

Crossrefs

Cf. A005117, A013929, A000040, A001359, A014574, A061398, A061399.

Sequence in context: A134449 A103579 A161500 * A126107 A193901 A083472

Adjacent sequences: A061348 A061349 A061350 * A061352 A061353 A061354

Keyword

nonn

Author

Labos Elemer, Jun 07 2001

Status

approved