



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
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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_13) > lpf(N_11) >= prime(n) and numbers N_2 for which lpf(N_21) > lpf(N_23) >= prime(n), if {N_23, N_21} is not a pair of twin primes, where p_n=prime(n) and lpf=least prime factor (A020639). (Cf., for example, A243803A243804). 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

Table of n, a(n) for n=1..57.
V. Shevelev, Theorems on twin primesdual case, arXiv:0912.4006 [math.GM], 20092014 (Section 14).


MATHEMATICA

lpf[k_] := FactorInteger[k][[1, 1]];
a19[n_ /; n>1] := a19[n] = For[k = If[n == 2, 10, a19[n1]], True, k = k+2, If[lpf[k3] > lpf[k1] >= Prime[n], Return[k]]];
a20[n_ /; n>1] := a20[n] = For[k = If[n <= 2, 2, a20[n1]], True, k = k+2, If[Not[PrimeQ[k3] && PrimeQ[k1]] && lpf[k1] > lpf[k3] >= Prime[n], Return[k]]];
Select[Range[250], a19[#] > a20[#]&] (* JeanFrançois 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



