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

1,2

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

Links

Table of n, a(n) for n=1..10.

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.

Example

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.

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]]]]

Prog

(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

Crossrefs

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

Sequence in context: A271018 A145638 A361567 * A012595 A012294 A219811

Adjacent sequences: A067662 A067663 A067664 * A067666 A067667 A067668

Keyword

more,nonn

Author

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

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

Status

approved