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A061351
Between p and the next prime either there are no numbers or there is a single squarefree number.
2
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 07 2001
STATUS
approved