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 A242720 Smallest even k such that the pair {k-3,k-1} is not a twin prime pair and lpf(k-1) > lpf(k-3) >= prime(n), where lpf = least prime factor (A020639). 29
 12, 38, 80, 212, 224, 440, 440, 854, 1250, 1460, 1742, 2282, 2282, 3434, 4190, 4664, 4760, 4760, 6890, 8054, 8054, 8054, 12374, 12830, 12830, 13592, 13592, 14282, 17402, 17402, 18212, 22502, 22502, 22502, 25220, 28202, 28202, 32234, 32402, 32402, 38012 (list; graph; refs; listen; history; text; internal format)
 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)

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Last modified April 6 11:51 EDT 2020. Contains 333273 sequences. (Running on oeis4.)