OFFSET
1,1
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jul 10 2014
EXTENSIONS
More terms from Peter J. C. Moses, Jul 10 2014
STATUS
approved