A243937 Even numbers n>=6 for which lpf(n-1) > lpf(n-3), where lpf = least prime factor.

6, 8, 12, 14, 18, 20, 24, 30, 32, 36, 38, 42, 44, 48, 54, 60, 62, 66, 68, 72, 74, 78, 80, 84, 90, 96, 98, 102, 104, 108, 110, 114, 120, 122, 126, 128, 132, 138, 140, 144, 150, 152, 156, 158, 162, 164, 168, 174, 180, 182, 186, 188, 192, 194, 198, 200, 204, 210

Offset: 1

Author

Vladimir Shevelev, Jul 10 2014

Keywords

• nonn

Comments

Complement of A245024 over even n >= 6.

Conjecture: All differences are 2, 4 or 6 such that there are no two consecutive terms 2 (..., 2, 2, ...), no two consecutive terms 4, while consecutive terms 6 occur 1, 2, 3 or 4 times; also consecutive pairs of terms 2, 4 appear 1, 2, 3 or 4 times. The conjecture is verified up to n = 2.5*10^7. - Vladimir Shevelev and Peter J. C. Moses, Jul 11 2014

Divisibility by 3 means 6m is in the sequence for all m > 0, and 6m + 4 never is, while 6m + 2 is undetermined. Divisibility by 5 means 30m + 8 is always in the sequence, and 30m + 26 never is. This proves the above conjecture. - Jens Kruse Andersen, Aug 19 2014

Note that,

1) Since numbers of the form 6*k evidently are in the sequence, then the counting function of the terms not exceeding x is not less than x/6.

2) Sequence {a(n)-1} contains all primes greater than 3 in the natural order. The subsequence of other terms of {a(n)-1} is 35, 65, 77, 95, ... - Vladimir Shevelev, Jul 15 2014

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A242719, A242720, A245024.

Programs

PARI

select(n->factor(n-1)[1,1]>factor(n-3)[1,1], vector(200, x, 2*x+4)) \\ Jens Kruse Andersen, Aug 19 2014

Extensions

More terms from Peter J. C. Moses, Jul 10 2014