OFFSET
1,1
COMMENTS
By the definition, either a(n)==1 (mod 3) or, for every pair of primes (p,q), p>q>=3, a(n)==1 (mod p) and a(n) not==3 (mod q).
Conjecture: All differences are 2,4 or 6 such that 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 4,2 appear 1,2,3 or 4 times.
Conjecture is verified up to n = 2.5*10^7. - Vladimir Shevelev and Peter J. C. Moses, Jul 11 2014
The first comment is wrong as stated. This would fix it: for every pair of primes (p,q), p>q>=3, if a(n)==1 (mod p) then a(n) not==3 (mod q). Divisibility by 3 means 6m+4 is in the sequence for all m>0, and 6m never is, while 6m+2 is undetermined. Divisibility by 5 means 30m+26 is always in the sequence, and 30m+8 never is. This proves the above conjecture. - Jens Kruse Andersen, Jul 13 2014
Note that the sequence {a(n)-3} contains all odd primes, except for lesser primes in twin primes pairs (A001359). Other terms of {a(n)-3} are 25,49,55,85,91,... - Vladimir Shevelev, Jul 15 2014
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MAPLE
lpf:= n -> min(numtheory:-factorset(n)):
select(n -> lpf(n-1) < lpf(n-3), [seq(2*k, k=3..1000)]); # Robert Israel, Jul 15 2014
MATHEMATICA
lpf[n_] := FactorInteger[n][[1, 1]];
Reap[For[n = 6, n <= 300, n += 2, If[lpf[n-1] < lpf[n-3], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 25 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jul 10 2014
EXTENSIONS
More terms from Peter J. C. Moses, Jul 10 2014
STATUS
approved