OFFSET
1,1
COMMENTS
a(11) > 10^7. - M. F. Hasler, May 16 2017
a(19) > 7.5*10^12. - Giovanni Resta, Nov 12 2019
REFERENCES
M. F. Hasler, Posting to Sequence Fans Mailing List, May 06 2017
EXAMPLE
Omega(1..5) = (0, 1, 1, 2, 1), therefore the first run of 4 numbers with nondecreasing Omega (= A001222) starts at a(4) = 1.
Omega(4..7) = (2, 1, 2, 1), so the first run of 2 numbers with nondecreasing Omega starts at a(2) = 5.
A run of subsequent numbers with nondecreasing Omega is of length 1 if it consists of a single number n with Omega(n-1) > Omega(n) > Omega(n+1) (else n belongs to a run of length >= 2). This happens first for a(1) = 46.
MATHEMATICA
Prepend[#, Module[{k = 2}, While[Sign@ Differences@ PrimeOmega[k + {-1, 0, 1}] != {-1, -1}, k++]; k]] &@ Function[s, Function[r, If[Length@ # > 0, #[[1, 1]], -1] &@ Select[s, Length@ # == r &]] /@ Range@ Max@ Map[Length, s]]@ DeleteCases[SplitBy[MapIndexed[Function[k, (2 Boole[#1 <= #2] - 1) k & @@ #1]@ First@ #2 &, Partition[Array[PrimeOmega, 10^7], 2, 1]], Sign], w_ /; First@ w < 0] (* Michael De Vlieger, May 19 2017 *)
PROG
(PARI)
alias('A, 'A286288); \\ A bug in PARI 2.9.2 requires the alias() to be issued on a line on itself.
A=vector(19); apply(scan(N, s=1, t=bigomega(s))=for(k=s+1, N, t>(t=bigomega(k))||next; k-s>#A||A[k-s]||printf(" a(%d)=%d, ", k-s, s)||A[k-s]=s; s=k); done, [1e7]) \\ Then the search may be extended using scan(END, START).
\\ M. F. Hasler, May 16 2017
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
N. J. A. Sloane, May 16 2017
EXTENSIONS
Edited by M. F. Hasler, May 16 2017
a(11)-a(13) from Jon E. Schoenfield, Jul 16 2017
a(14)-a(18) from Giovanni Resta, Nov 12 2019
STATUS
approved