A067665 The start of a record-setting run of consecutive integers i with distinct A001222(i).

1, 6, 15, 60, 726, 6318, 189375, 755968, 683441871, 33714015615

Offset: 1

Author

G. L. Honaker, Jr., Feb 03 2002

Keywords

• more
• nonn

Comments

The list of indices of record terms in A068796;

n is in the sequence if A068796(n) is larger than A068796(m) when n is larger than m. For the known terms, f(a(n)) = n+1. Is that true for all n? In other words, is the monotonic subsequence of A068796 identical to A020725?

a(11) > 10^13. - Giovanni Resta, Jan 08 2014

Examples

			The values of f(n) for n=1 to 15 are 2,1,2,2,2,3,3,2,1,3,2,3,2,1,4. Records occur at f(1)=2, f(6)=3 and f(15)=4.
		

Links

• J.-M. De Koninck, J. B. Friedlander, and F. Luca, On strings of consecutive integers with a distinct number of prime factors, Proc. Amer. Math. Soc., 137 (2009), 1585-1592.

Crossrefs

Cf. A001222, A067650, A068069, A068796, A068797.

Programs

Mathematica

bigomega[n_] := Plus@@Last/@FactorInteger[n]; f[n_] := For[k=1; s={bigomega[n]}, True, k++, If[MemberQ[s, z=bigomega[n+k]], Return[k], AppendTo[s, z]]]; For[n=1; max=0, True, n++, If[f[n]>max, Print[n, " ", max=f[n]]]]

PARI

a(n,lim=1e12,startAt=1)={
  forstep(i=startAt-1,lim,10^6-n,
    my(v=vectorsmall(min(10^6,lim\1-i),j,bigomega(j+i)));
    for(j=n,#v,if(#vecsort(v[j-n+1..j],,8)==n,return(j+i-n+1)))
  )
}; \\ Charles R Greathouse IV, Jul 03 2013

Extensions

More terms from Shyam Sunder Gupta, Feb 08 2002

Edited by Robert G. Wilson v, Feb 20 2002

Edited by Dean Hickerson, Mar 05 2002

a(10) from Donovan Johnson, Oct 15 2008