|
| |
|
|
A067665
|
|
The start of a record-setting run of consecutive integers i with distinct A001222(i).
|
|
4
| | |
|
|
|
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?
|
|
|
REFERENCES
| 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. DOI:10.1090/S0002-9939-08-09702-5
|
|
|
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]]]]
|
|
|
CROSSREFS
| Cf. A001222, A067650, A068069, A068796, A068797.
Sequence in context: A190801 A093042 A145638 * A012595 A012294 A069750
Adjacent sequences: A067662 A067663 A067664 * A067666 A067667 A067668
|
|
|
KEYWORD
| more,nonn
|
|
|
AUTHOR
| G. L. Honaker, Jr. (honak3r(AT)gmail.com), Feb 03 2002
|
|
|
EXTENSIONS
| More terms from Shyam Sunder Gupta (guptass(AT)rediffmail.com), Feb 08 2002
Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 20 2002; and by Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 05 2002
a(10) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 15 2008
|
| |
|
|
