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A214343 a(n) is the smallest integer j such that the numbers of prime factors (counting multiplicity) in j, j+1, ... , j+n-1 are the full set {1,2,...,n}. 1
2, 3, 6, 15, 77, 726, 6318, 189375, 755968, 871593371, 33714015615 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Next term a(10) > 5*10^7. Joerg Arndt, Jul 14 2012

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

a(4)=15 because 15 has two prime factors, 16 has four, 17 has one and 18 has three (and 15 is the smallest number with this property).

a(5) = 77 because 77, 78, 79, 80 and 81 have 2, 3, 1, 5 and 4 prime factors.

MAPLE

A214343 := proc(n)

    refs := {seq(i, i=1..n)} ;

    for j from 1 do

        pf := {} ;

        for k from 0 to n-1 do

            pf := pf union {numtheory[bigomega](j+k)} ;

            if nops(pf) < k+1 then

                break;

            end if;

        end do:

        if pf = refs then

            return j;

        end if;

    end do:

end proc: # R. J. Mathar, Jul 13 2012

MATHEMATICA

f[n_] := f[n] = FactorInteger[n][[All, 2]] // Total;

n = 1;

i = 2;

While[True,

  While[Union[Table[f[j], {j, i, i + n - 1}]] != Range[n],

   i += 1; f[i] =.

   ];

  Print[i]; n += 1;

  ];

CROSSREFS

Cf. A072875, A001222.

Sequence in context: A001529 A069354 A116632 * A007364 A305857 A014627

Adjacent sequences:  A214340 A214341 A214342 * A214344 A214345 A214346

KEYWORD

nonn

AUTHOR

Jake Foster, Jul 13 2012

EXTENSIONS

a(10)-a(11) from Donovan Johnson, Jul 15 2012

STATUS

approved

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Last modified September 30 12:50 EDT 2022. Contains 357105 sequences. (Running on oeis4.)