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).

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

Offset: 2

Author

Vladimir Shevelev, May 16 2014

Keywords

• nonn

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 {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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001359, A006512, A242489.

Programs

PARI

a(n)=my(p=prime(n),k=p+3); while(factor(k-3)[1,1]
Charles R Greathouse IV, May 30 2014

Extensions

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