The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A289995 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A289995

Numbers n with omega(n) <= 1 such that omega(n+1) = 1 or omega(n+2) = 1.
(history; published version)

#39 by Harvey P. Dale at Thu Jul 04 14:13:13 EDT 2019

STATUS

editing

approved

#38 by Harvey P. Dale at Thu Jul 04 14:13:09 EDT 2019

MATHEMATICA

onQ[{a_, b_, c_}]:=a<2&&(b==1||c==1); SequencePosition[PrimeNu[ Range[ 1100]], _?onQ][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 04 2019 *)

STATUS

approved

editing

#37 by Charles R Greathouse IV at Thu Sep 21 15:38:12 EDT 2017

STATUS

editing

approved

#36 by Charles R Greathouse IV at Thu Sep 21 15:38:09 EDT 2017

FORMULA

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 21 2017

STATUS

approved

editing

#35 by Charles R Greathouse IV at Thu Sep 21 15:37:25 EDT 2017

STATUS

editing

approved

#34 by Charles R Greathouse IV at Thu Sep 21 15:37:17 EDT 2017

LINKS

Charles R Greathouse IV, <a href="/A289995/b289995.txt">Table of n, a(n) for n = 1..10000</a>

PROG

(PARI) list(lim)=my(v=List([1]), p=3, t); forprime(q=5, lim+2, if(q-p<3, listput(v, p)); p=q); for(e=1, logint(lim\=1, 2), t=2^e; if(isprimepower(t-1), listput(v, t-1)); if(isprimepower(t+1), listput(v, t))); for(e=2, logint(lim, 3), forprime(q=2, 3, sqrtnint(lim, e), t=q^e; if(isprimepower(t-2), listput(v, t-2)); if(isprimepower(t+2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Sep 21 2017

#33 by Charles R Greathouse IV at Thu Sep 21 15:35:26 EDT 2017

PROG

(PARI) is(n)=if(n<6, n>0, isprimepower(n) && (isprimepower(n+2) || isprimepower(n+1))) \\ Charles R Greathouse IV, Sep 21 2017

(PARI) list(lim)=my(v=List([1]), p=3, t); forprime(q=5, lim+2, if(q-p<3, listput(v, p)); p=q); for(e=1, logint(lim\=1, 2), t=2^e; if(isprimepower(t-1), listput(v, t-1)); if(isprimepower(t+1), listput(v, t))); for(e=2, logint(lim, 3), forprime(q=2, sqrtnint(lim, e), t=q^e; if(isprimepower(t-2), listput(v, t-2)); if(isprimepower(t+2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Sep 21 2017

STATUS

approved

editing

#32 by Alois P. Heinz at Mon Sep 18 11:21:17 EDT 2017

STATUS

editing

approved

#31 by Alois P. Heinz at Mon Sep 18 11:20:35 EDT 2017

EXAMPLE

n=125 is in the sequence, since omega(125) = 1 and omega(125+2) = 1;

n=127 is in the sequence, since omega(127) = 1 and omega(127+1) = 1.

MATHEMATICA

Select[Range[3000], PrimeNu[#]<=1&&(PrimeNu[#+1]==1||PrimeNu[#+2]==1)&] (*_ _Peter J. C. Moses_, Sep 03 2017 *)

KEYWORD

nonn,changed

nonn

STATUS

reviewed

editing

#30 by Peter Luschny at Mon Sep 18 11:20:26 EDT 2017

STATUS

proposed

reviewed