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A354604 Midpoints of record gaps between primes: a(n) = (A000101(n) + A002386(n))/2 for n > 1.

%I A354604 #28 Apr 21 2025 08:35:33
%S A354604 4,9,26,93,120,532,897,1140,1344,9569,15705,19635,31433,155964,360701,
%T A354604 370317,492170,1349592,1357267,2010807,4652430,17051797,20831428,
%U A354604 47326803,122164858,189695776,191912907,387096258,436273150,1294268635,1453168287,2300942709,3842610941,4302407536,10726904850,20678048489,22367085156,25056082315,42652618575
%N A354604 Midpoints of record gaps between primes: a(n) = (A000101(n) + A002386(n))/2 for n > 1.
%C A354604 In the displayed portion of the sequence, the only numbers of least prime signature (A025487) are 4 and 120. This is noteworthy because numbers of least prime signature frequently are adjacent to primes (see A344385). It appears to be far more rare for a number of least prime signature to be at the center of a maximal prime gap. With 4 being a term in A344385, 120 seems to have a unique status. - _Hal M. Switkay_, Mar 13 2025
%H A354604 Hugo Pfoertner, <a href="/A354604/b354604.txt">Table of n, a(n) for n = 2..83</a>
%H A354604 Hugo Pfoertner, <a href="/plot2a?name1=A354604&amp;name2=A005250&amp;tform1=log+base+10&amp;tform2=log+base+10&amp;shift=0&amp;radiop1=xy&amp;drawpoints=true">Gap sizes vs location</a>, using Plot 2.
%Y A354604 Subsequence of A024675.
%Y A354604 Cf. A000040, A000101, A002386, A344385.
%K A354604 nonn
%O A354604 2,1
%A A354604 _Donghwi Park_, Jul 08 2022