

A286287


Least number to start a run of exactly n nondecreasing values of little omega (A001221).


6



106, 11, 13, 7, 512, 1, 1941, 141, 6847, 211, 195031, 82321, 808083, 534077, 3355906, 526093, 526889774, 127890361, 22529949392, 118968284927, 164159173895, 244022049199, 3022058317713, 585927201061
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OFFSET

1,1


COMMENTS

a(17) > 10^7.
a(18) = 127890361; a(n) > 4*10^8 for n=17 and for n >= 19.  Jon E. Schoenfield, Jul 16 2017


REFERENCES

M. F. Hasler, Posting to Sequence Fans Mailing List, May 06 2017


LINKS



EXAMPLE

We have omega(10) = 2, omega(11) = 1, omega(12) = 2, omega(13) = 1. Therefore 11 starts a run of exactly 2 consecutive integers (11, 12) which have nondecreasing (here: strictly increasing) values of omega.
The 6 numbers from 1 through 6 yield values (0, 1, ..., 1, 2) for omega, therefore a(6) = 1. The 4 numbers from 7 through 10 yield values (1, 1, 1, 2) for omega, therefore a(4) = 7.
A run of length 1 is a single number n such that omega(n1) > omega(n) > omega(n+1). (If we had "<=" in one of the cases, it would be part of a run of at least 2 numbers with nondecreasing omega.) This first happens for a(1) = 106.


MATHEMATICA

Prepend[#, Module[{k = 2}, While[Sign@ Differences@ PrimeNu[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[PrimeNu, 10^7], 2, 1]], Sign], w_ /; First@ w < 0] (* Michael De Vlieger, May 19 2017 *)


PROG

(PARI) alias("A", "A286287"); A=vector(19); apply(scan(N, s=1, t=omega(s))=for(k=s+1, N, t>(t=omega(k))next; ks>#AA[ks]printf(" a(%d)=%d, ", ks, s)A[ks]=s; s=k); done, [4e6]) \\ Then the search may be extended using scan(END, START).  M. F. Hasler, May 16 2017


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



