A239674 -id:A239674 - cp's OEIS frontend

A085809 Indices of semiprimes where largest gap occurs. Or, positions of records in A065516.

1, 2, 4, 6, 10, 34, 186, 422, 760, 1765, 4112, 4585, 8112, 8650, 8861, 75150, 223993, 327048, 712605, 1135940, 23958638, 42367759, 47848742, 54626559, 121984495, 157877985, 413509327, 798321315, 983679985, 1277946119, 2403158480

Offset: 1

Jason Earls, Jul 24 2003

nonn

A215231(n) = A065516(a(n)). - Reinhard Zumkeller, Mar 23 2014

Cf. A239674.

a085809 n = a085809_list !! (n-1)
-- See A215231 for definition of a085809_list.
-- Reinhard Zumkeller, Mar 23 2014

{sgr(m)=local(a,b,rec,c); c=0; a=0; b=4; rec=0; for(n=5,m,if(bigomega(n)==2,c++; a=n; if(a-b>rec,rec=a-b; print1(c","); b=a,b=a; )))}

a(19)-a(26) from Donovan Johnson, Jan 28 2009

a(27)-a(31) from Donovan Johnson, Apr 14 2010

A239656 First differences of sphenic numbers, cf. A007304.

Original entry on oeis.org

12, 24, 4, 8, 24, 3, 5, 4, 16, 8, 16, 11, 5, 4, 8, 4, 4, 5, 27, 8, 1, 7, 8, 9, 3, 8, 7, 9, 3, 1, 4, 20, 8, 4, 23, 9, 3, 9, 4, 4, 11, 14, 3, 4, 4, 8, 8, 3, 1, 4, 1, 3, 4, 13, 10, 5, 4, 9, 11, 4, 8, 12, 12, 4, 21, 6, 13, 8, 8, 5, 3, 4, 4, 3, 1, 5, 3, 9, 11, 4

Offset: 1

Reinhard Zumkeller, Mar 23 2014

nonn

a(n) = A007304(n+1) - A007304(n);

see A239673 and A239674 for record values and where they occur: A239673(n) = a(A239674(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A065516.

a239656 n = a239656_list !! (n-1)
a239656_list = zipWith (-) (tail a007304_list) a007304_list

A007304 := proc(n)
    option remember;
    if n = 1 then
        30;
    else
        for a from procname(n-1)+1 do
            if numtheory[bigomega](a) =3 and nops(numtheory[factorset](a)) = 3 then
                return a;
            end if;
        end do:
    end if;
end proc:
A239656 := proc(n)
    A007304(n+1)-A007304(n) ;
end proc:

With[{upto=1000},Differences[Sort[Select[Times@@@Subsets[Prime[ Range[ Ceiling[upto/6]]],{3}],#<=upto&]]]] (* Harvey P. Dale, Jan 08 2015 *)

A239673 Record values in A239656 (the first differences of sphenic numbers).

Original entry on oeis.org

12, 24, 27, 28, 33, 35, 43, 44, 46, 48, 50, 52, 60, 65, 70, 72, 79, 82, 92, 98

Offset: 1

Reinhard Zumkeller, Mar 23 2014

Cf. A007304, A005250, A215231, A239656, A239674.

a239673 n = a239673_list !! (n-1)
(a239673_list, a239674_list) = unzip $ (12, 1) : f 1 12 a239656_list where
   f i v (q:qs) | q > v = (q, i) : f (i + 1) q qs
                | otherwise = f (i + 1) v qs
-- Reinhard Zumkeller, Mar 23 2014

lista(kmax) = {my(k1 = 30, d, dm = 0); forcomposite(k2 = k1 + 1, kmax, if(factor(k2)[,2] == [1,1,1]~, d = k2 - k1; if(d > dm, dm = d; print1(d, ", ")); k1 = k2));} \\ Amiram Eldar, May 19 2024

a(n) = A239656(A239674(n)).

a(12)-a(20) from Amiram Eldar, May 19 2024

cp's OEIS Frontend

A085809 Indices of semiprimes where largest gap occurs. Or, positions of records in A065516.

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A239656 First differences of sphenic numbers, cf. A007304.

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A239673 Record values in A239656 (the first differences of sphenic numbers).

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