OFFSET
2,1
COMMENTS
The sequence is nondecreasing. See comment in A242758.
a(n) >= prime(n)^2+3. Conjecture: a(n) <= prime(n)^4. - Vladimir Shevelev, Jun 01 2014
Conjecture. There are only a finite number of composite numbers of the form a(n)-1. Peter J. C. Moses found only two: a(16)-1 = 4189 = 59*71 and a(20)-1 = 6889 = 83^2 and no others up to a(2501). Most likely, there are no others. - Vladimir Shevelev, Jun 09 2014
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 2..2501
V. Shevelev, Theorems on twin primes-dual case, arXiv:0912.4006 [math.GM], 2009-2014, (Section 10).
FORMULA
Conjecturally, a(n) ~ (prime(n))^2, as n goes to infinity (cf. A246748, A246821). - Vladimir Shevelev, Sep 02 2014
For n>=3, a(n) >= (prime(n)+1)^2 + 2. Equality holds for terms of A246824. - Vladimir Shevelev, Sep 04 2014
MATHEMATICA
lpf[n_] := FactorInteger[n][[1, 1]];
Clear[a]; a[n_] := a[n] = For[k = If[n <= 2, 2, a[n-1]], True, k = k+2, If[Not[PrimeQ[k-3] && PrimeQ[k-1]] && lpf[k-1] > lpf[k-3] >= Prime[n], Return[k]]];
Table[a[n], {n, 2, 50}] (* Jean-François Alcover, Nov 02 2018 *)
PROG
(PARI)
lpf(k) = factorint(k)[1, 1];
vector(60, n, k=6; while((isprime(k-3) && isprime(k-1)) || lpf(k-1)<=lpf(k-3) || lpf(k-3)<prime(n+1), k+=2); k) \\ Colin Barker, Jun 01 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 21 2014
STATUS
approved