

A030296


Smallest start for a run of at least n composite numbers.


4



4, 8, 8, 24, 24, 90, 90, 114, 114, 114, 114, 114, 114, 524, 524, 524, 524, 888, 888, 1130, 1130, 1328, 1328, 1328, 1328, 1328, 1328, 1328, 1328, 1328, 1328, 1328, 1328, 9552, 9552, 15684, 15684, 15684, 15684, 15684, 15684, 15684, 15684, 19610, 19610, 19610
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OFFSET

1,1


COMMENTS

a(n) is even, since a(n)1 is a prime > 2, by the minimality of a(n).  Jonathan Sondow, May 31 2014
Except for a(1), records occur at even values of n, and each term appears an even number of times consecutively. (Proof. A maximal run of composites must begin and end at even numbers.)  Jonathan Sondow, May 31 2014


REFERENCES

Amarnath Murthy, Some more conjectures on primes and divisors, Smarandache Notions Journal, Vol. 12, No. 123, Spring 2001.


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1475 (terms < 4*10^18)
Thomas R. Nicely, First occurrence prime gaps
Eric Weisstein's World of Mathematics, Prime Gaps


FORMULA

a(n) = A104138(n) + 1.  Jonathan Sondow, May 31 2014


EXAMPLE

a(5) = 24 as 24 is the first of the five consecutive composite numbers 24, 25, 26, 27, 28.


MATHEMATICA

a[n_] := a[n] = For[p1 = a[n1]1; p2 = NextPrime[p1], True, p1 = p2; p2 = NextPrime[p1], If[ p2p11 >= n, Return[p1+1]]]; a[1] = 4; Table[a[n], {n, 1, 43}] (* JeanFrançois Alcover, May 24 2012 *)


CROSSREFS

Cf. A008950, A008995, A008996, A000101, A002386, A104138.
Sequence in context: A141800 A019197 A066106 * A160171 A195752 A095806
Adjacent sequences: A030293 A030294 A030295 * A030297 A030298 A030299


KEYWORD

nonn,nice


AUTHOR

Eric W. Weisstein


STATUS

approved



