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A286288 Least number to start a run of exactly n nondecreasing values of (big) Omega (A001222). 5
46, 5, 43, 1, 2021, 121, 25202, 2521, 162121, 460801, 27268546, 23553169, 244068841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(11) > 10^7. - M. F. Hasler, May 16 2017

REFERENCES

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

LINKS

Table of n, a(n) for n=1..13.

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 in 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) From M. F. Hasler, May 16 2017: (Start)

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). - (End)

CROSSREFS

Cf. A001222, A284597 (analog for sigma_0 = A000005), A285893 (analog for sigma = A000203), A286287 (analog for omega = A001221).

See also A286289.

Sequence in context: A036204 A270814 A284597 * A051161 A260512 A033366

Adjacent sequences:  A286285 A286286 A286287 * A286289 A286290 A286291

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

STATUS

approved

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Last modified November 17 08:17 EST 2018. Contains 317275 sequences. (Running on oeis4.)