

A242490


Smallest even number k such that lpf(k3) = prime(n) while lpf(k1) > lpf(k3), where lpf=least prime factor (A020639).


8



6, 8, 80, 14, 224, 20, 440, 854, 32, 1460, 1742, 44, 2282, 3434, 4190, 62, 5432, 4760, 74, 12194, 8930, 8054, 12374, 13292, 104, 15350, 110, 14282, 31982, 17402, 18212, 140, 24050, 152, 25220, 29990, 28202, 32234, 33392, 182, 43262, 194, 44972, 200, 47564
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OFFSET

2,1


COMMENTS

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.
If we change the definition to consider k for which {k3, k1} 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


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 2..1001


EXAMPLE

Let n=2, prime(2)=3. Then lpf(63)=3, but lpf(61)=5>3. Since k=6 is the smallest such k, a(2)=6.


PROG

(PARI) a(n)=my(p=prime(n), k=p+3); while(factor(k3)[1, 1]<p  factor(k1)[1, 1]<p, k += 2*p); k \\ Charles R Greathouse IV, May 30 2014


CROSSREFS

Cf. A001359, A006512, A242489.
Sequence in context: A270038 A284635 A250256 * A216796 A137127 A013241
Adjacent sequences: A242487 A242488 A242489 * A242491 A242492 A242493


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, May 16 2014


EXTENSIONS

Correction and more terms from Peter J. C. Moses, May 19 2014


STATUS

approved



