cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A242621 Start of the least triple of consecutive squarefree numbers each of which has exactly n distinct prime factors.

Original entry on oeis.org

2, 33, 1309, 27962, 3323705, 296602730, 41704979953
Offset: 1

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Author

M. F. Hasler, May 18 2014

Keywords

Comments

As the example of a(4)=27962 shows, "consecutive squarefree numbers" means consecutive elements of A005117, not necessarily consecutive integers that (additionally) are squarefree; this would be a more restrictive condition.
a(8) <= 102099792179229 because A093550 - 1 is an upper bound of the present sequence.

Examples

			The two squarefree numbers following a(4)=27962, namely, 27965 and 27966, also have 4 prime divisors just as a(4).

Links

Crossrefs

See A242605-A242608 for triples of consecutive squarefree numbers with m=2,..,5 prime factors.
See A246470 for the quadruplet and A246548 for the 5-tuple versions of this sequence.
See A039833, A066509, A176167 and A192203 for triples of consecutive numbers which are squarefree and have m=2,..,5 prime factors.

Extensions

Edited and a(6)-a(7) added by Hans Havermann, Aug 27 2014

A246470 Start of the least quadruplet of consecutive squarefree numbers each of which has exactly n distinct prime factors.

Original entry on oeis.org

4058471, 91, 3854, 178086, 15469622, 18230787183
Offset: 1

Views

Author

Hans Havermann, Aug 27 2014

Keywords

Comments

By "consecutive squarefree numbers" we mean consecutive terms of A005117, not consecutive integers that also happen to be squarefree.

Examples

			4058471, 4058473, 4058477, and 4058479 are the smallest 4 primes that are also consecutive squarefree numbers (4058472 = 2^3*3*11*15373, 4058474 = 2*7^2*41413, 4058475 = 3*5^2*53*1021, 4058476 = 2^2*19*53401, and 4058478 = 2*3^3*17*4421), so a(1) = 4058471.
91, 93, 94, and 95 are the smallest 4 semiprimes that are also consecutive squarefree numbers, so a(2) = 91.
3854, 3855, 3857, and 3858 is the smallest 4-tuple of consecutive squarefree numbers each of which has exactly 3 prime factors, so a(3) = 3854.

Crossrefs

Cf. A005117, A242621 (triple version), A246548 (5-tuple version), A246471.

A246471 First of the least n primes that are also consecutive terms of A005117 (squarefree numbers).

Original entry on oeis.org

2, 2, 2, 4058471, 462807341
Offset: 1

Views

Author

Hans Havermann, Aug 27 2014

Keywords

Comments

a(6) > 10^11.
a(6) <= 10211143417747. - Jens Kruse Andersen, Sep 09 2014
If the k-tuple conjecture is true then a(n) always exists. Weak upper bounds are
a(7) <= 105629504093565907896809
a(8) <= 9921941384213872059341198331469403
a(9) <= 376847848512740851019714299079899219399
a(10) <= 32108207632017215023964871615662539298039357
- Jens Kruse Andersen, Sep 10 2014

Examples

			Trivially, primes 2, 3, and 5 are consecutive squarefree numbers so a(1)-a(3) are each 2.
4058471, 4058473, 4058477, and 4058479 are the least 4 primes that are also consecutive squarefree numbers (4058472 = 2^3*3*11*15373, 4058474 = 2*7^2*41413, 4058475 = 3*5^2*53*1021, 4058476 = 2^2*19*53401, and 4058478 = 2*3^3*17*4421) so a(4) = 4058471.

Crossrefs

Cf. A005117; a(3) is first term in A242621; a(4) is first term in A246470; a(5) is first term in A246548.
Showing 1-3 of 3 results.

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