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 A242490 Smallest even number k such that lpf(k-3) = prime(n) while lpf(k-1) > lpf(k-3), where lpf=least prime factor (A020639). 8

%I

%S 6,8,80,14,224,20,440,854,32,1460,1742,44,2282,3434,4190,62,5432,4760,

%T 74,12194,8930,8054,12374,13292,104,15350,110,14282,31982,17402,18212,

%U 140,24050,152,25220,29990,28202,32234,33392,182,43262,194,44972,200,47564

%N Smallest even number k such that lpf(k-3) = prime(n) while lpf(k-1) > lpf(k-3), where lpf=least prime factor (A020639).

%C Note that the "small terms" {6,8,14,20,32,44,...} correspond to a(n) for which {a(n)-3, a(n)-1} is a twin pair such that the corresponding positions form sequence A029707.

%C If we change the definition to consider k for which {k-3, k-1} is not a twin pair, we obtain a closely related sequence 12,38,80,212,224,530,440,854,1250,1460,1742,... which shows a "model behavior" of A242490, if there are only a finite number of twin primes. - _Vladimir Shevelev_, May 19 2014

%H Peter J. C. Moses, <a href="/A242490/b242490.txt">Table of n, a(n) for n = 2..1001</a>

%e Let n=2, prime(2)=3. Then lpf(6-3)=3, but lpf(6-1)=5>3. Since k=6 is the smallest such k, a(2)=6.

%o (PARI) a(n)=my(p=prime(n),k=p+3); while(factor(k-3)[1,1]<p || factor(k-1)[1,1]<p, k += 2*p); k \\ _Charles R Greathouse IV_, May 30 2014

%Y Cf. A001359, A006512, A242489.

%K nonn

%O 2,1

%A _Vladimir Shevelev_, May 16 2014

%E Correction and more terms from _Peter J. C. Moses_, May 19 2014

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Last modified October 14 07:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)