|
%I #27 Mar 16 2015 22:34:20
%S 1,6,15,60,726,6318,189375,755968,683441871,33714015615
%N The start of a record-setting run of consecutive integers i with distinct A001222(i).
%C The list of indices of record terms in A068796;
%C 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?
%C a(11) > 10^13. - _Giovanni Resta_, Jan 08 2014
%H J.-M. De Koninck, J. B. Friedlander, and F. Luca, <a href="http://dx.doi.org/10.1090/S0002-9939-08-09702-5">On strings of consecutive integers with a distinct number of prime factors</a>, Proc. Amer. Math. Soc., 137 (2009), 1585-1592.
%e 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.
%t 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]]]]
%o (PARI) a(n,lim=1e12,startAt=1)={
%o forstep(i=startAt-1,lim,10^6-n,
%o my(v=vectorsmall(min(10^6,lim\1-i),j,bigomega(j+i)));
%o for(j=n,#v,if(#vecsort(v[j-n+1..j],,8)==n,return(j+i-n+1)))
%o )
%o }; \\ _Charles R Greathouse IV_, Jul 03 2013
%Y Cf. A001222, A067650, A068069, A068796, A068797.
%K more,nonn
%O 1,2
%A _G. L. Honaker, Jr._, Feb 03 2002
%E More terms from _Shyam Sunder Gupta_, Feb 08 2002
%E Edited by _Robert G. Wilson v_, Feb 20 2002
%E Edited by _Dean Hickerson_, Mar 05 2002
%E a(10) from _Donovan Johnson_, Oct 15 2008
|
