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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 (list; graph; refs; listen; history; text; internal format)
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. 1-2-3, 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[n-1]-1; p2 = NextPrime[p1], True, p1 = p2; p2 = NextPrime[p1], If[ p2-p1-1 >= n, Return[p1+1]]]; a[1] = 4; Table[a[n], {n, 1, 43}] (* Jean-Fran├žois 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

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Last modified March 24 01:20 EDT 2019. Contains 321444 sequences. (Running on oeis4.)