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 A242719 Smallest even k such that lpf(k-3) > lpf(k-1) >= prime(n), where lpf=least prime factor (A020639). 29
 10, 26, 50, 170, 170, 362, 362, 842, 842, 1370, 1370, 1850, 1850, 2210, 3722, 3722, 3722, 4892, 5042, 7082, 7922, 7922, 7922, 10610, 10610, 10610, 11450, 13844, 16130, 16130, 17162, 19322, 19322, 24614, 24614, 25592, 29504, 29930, 29930, 36020, 36020 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The sequence is connected with a sufficient condition for the existence of an infinity of twin primes. In contrast to A242489, this sequence is nondecreasing. All even numbers of the form A062326(n)^2 + 1 are in the sequence. All a(n)-1 are semiprimes. - Vladimir Shevelev, May 24 2014 a(n) <= A242489(n); a(n) >= prime(n)^2+1. Conjecture: a(n) <= prime(n)^4. - Vladimir Shevelev, Jun 01 2014 Conjecture: all numbers a(n)-3 are primes. Peter J. C. Moses verified this conjecture up to a(2001) (cf. with conjecture in A242720). - Vladimir Shevelev, Jun 09 2014 LINKS Jinyuan Wang, Table of n, a(n) for n = 2..5000 (terms 2..2001 from Peter J. C. Moses). FORMULA Conjecturally, a(n) ~ (prime(n))^2, as n goes to infinity (cf. A246748, A246819). - Vladimir Shevelev, Sep 02 2014 a(n) = prime(n)^2 + 1 for and only for numbers n>=2 which are in A137291. - Vladimir Shevelev, Sep 04 2014 MATHEMATICA lpf[k_] := FactorInteger[k][[1, 1]]; a[n_] := a[n] = For[k = If[n == 2, 10, a[n-1]], True, k = k+2, If[lpf[k-3] > lpf[k-1] >= Prime[n], Return[k]]]; Array[a, 50, 2] (* Jean-François Alcover, Nov 06 2018 *) PROG (PARI) lpf(k) = factorint(k)[1, 1]; vector(50, n, k=6; while(lpf(k-3)<=lpf(k-1) || lpf(k-1)

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)