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Search: id:A061351
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| A061351 |
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Between p and the next prime either there are no numbers or there is a single square-free number. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Apart from the initial 2, the lesser of twin primes {p, p+2} such that the middle term p+1 is square-free: intersection[{A014574(n)},{A005117(n)}]
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
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EXAMPLE
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Between 29 and 31 the only composite is 30, a square-free number. If next(p)-p>2, a non-square-free integer always arises between them.
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PROGRAM
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(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 ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 21 2009]
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CROSSREFS
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Cf. A005117, A013929, A000040, A001359, A014574, A061398, A061399.
Sequence in context: A134449 A103579 A161500 this_sequence A126107 A083472 A057794
Adjacent sequences: A061348 A061349 A061350 this_sequence A061352 A061353 A061354
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 07 2001
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