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 A242847 Numbers n for which A242719(n) > A242720(n). 7
 19, 35, 38, 41, 45, 50, 53, 56, 57, 58, 59, 63, 76, 77, 78, 79, 80, 81, 83, 84, 85, 92, 93, 95, 96, 108, 109, 112, 113, 116, 117, 124, 125, 126, 142, 143, 146, 154, 157, 173, 184, 185, 186, 193, 194, 195, 196, 197, 203, 215, 217, 224, 227, 232, 233, 237, 241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is infinite, in view of a strong closeness between counting functions of numbers N_1 for which lpf(N_1-3) > lpf(N_1-1) >= prime(n) and numbers N_2 for which lpf(N_2-1) > lpf(N_2-3) >= prime(n), if {N_2-3, N_2-1} is not a pair of twin primes, where p_n=prime(n) and lpf=least prime factor (A020639). (Cf., for example, A243803-A243804). This closeness is explained by a somewhat symmetry (for details, see Shevelev's link). However, it is very interesting to find an analytical proof of infinity of this and complementory sequences. LINKS V. Shevelev, Theorems on twin primes-dual case, arXiv:0912.4006 [math.GM], 2009-2014 (Section 14). MATHEMATICA lpf[k_] := FactorInteger[k][[1, 1]]; a19[n_ /; n>1] := a19[n] = For[k = If[n == 2, 10, a19[n-1]], True, k = k+2, If[lpf[k-3] > lpf[k-1] >= Prime[n], Return[k]]]; a20[n_ /; n>1] := a20[n] = For[k = If[n <= 2, 2, a20[n-1]], True, k = k+2, If[Not[PrimeQ[k-3] && PrimeQ[k-1]] && lpf[k-1] > lpf[k-3] >= Prime[n], Return[k]]]; Select[Range[250], a19[#] > a20[#]&] (* Jean-François Alcover, Nov 06 2018 *) CROSSREFS Cf. A242719, A242720, A242758. Sequence in context: A140601 A031206 A214231 * A044064 A044445 A166055 Adjacent sequences:  A242844 A242845 A242846 * A242848 A242849 A242850 KEYWORD nonn AUTHOR Vladimir Shevelev, Jun 02 2014 EXTENSIONS More terms from Peter J. C. Moses, Jun 02 2014 STATUS approved

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Last modified May 25 22:51 EDT 2022. Contains 354073 sequences. (Running on oeis4.)