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

2,1

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 {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

Links

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

Example

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.

Prog

(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

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