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A155764 Records in A047160.

%I A155764 #41 Jun 28 2025 22:11:08
%S A155764 0,1,3,9,15,18,21,27,33,39,42,45,48,75,87,93,117,120,135,138,168,183,
%T A155764 210,228,300,333,369,393,453,525,621,720,810,846,1086,1281,1305,1515,
%U A155764 1590,1617,1722,1794,1833,1851,2010,2064,2085,2112,2217,2352,2754,2784
%N A155764 Records in A047160.
%C A155764 Other than a(2)=1, every known term is a multiple of three. Equivalently, assuming A155765(n) - a(n) != 3, no term of A155765 is a multiple of three. - _Jason Kimberley_, Oct 24 2012
%C A155764 Conjecture 1: a(n) < 0.138*log(A155765(n))^3.6 for n > 4. Conjecture 2: If Conjecture 1 and Goldbach's conjecture hold, for any integer m > 22, there exist at least one pairs of primes m-d and m+d such that d < 0.138*log(m)^3.6. - _Ya-Ping Lu_, Nov 27 2020
%H A155764 Gilmar Rodriguez Pierluissi, <a href="/A155764/b155764.txt">Table of n, a(n) for n = 1..64</a> (terms 1..61 from T. D. Noe)
%H A155764 OEIS (Plot 2), <a href="/plot2a?name1=A155765&amp;name2=A155764&amp;tform1=log+base+10&amp;tform2=log+base+10&amp;shift=0&amp;radiop1=xy&amp;drawpoints=true">Plot of (log(A155765(n)), log(A155764(n)))</a> - _Jason Kimberley_, Oct 24 2012
%F A155764 a(n) = A047160(A155765(n)). - _Jason Kimberley_, Sep 01 2011
%t A155764 mgppp[n_?EvenQ]/;n>3:=Block[{m=PrimePi[n/2],p},While[!PrimeQ[n-(p=Prime[m])],m--];p];
%t A155764 dist[n_?EvenQ]:=Module[{d},{m=n/2,d=(m-mgppp[n])};d]
%t A155764 For[n=4;a=-1,True,n+=2,b=dist[n];If[b>a,Print[b];a=b]]
%t A155764 (* _Gilmar Rodriguez Pierluissi_, Aug 27 2018 *)
%o A155764 (Python)
%o A155764 from sympy import isprime
%o A155764 a_rec = -1
%o A155764 m = 2
%o A155764 while 1:
%o A155764     a = 0
%o A155764     while a < m - 1:
%o A155764         if isprime(m-a) == 1 and isprime(m+a) == 1:
%o A155764             if a > a_rec:
%o A155764                 print(a)
%o A155764                 a_rec = a
%o A155764             break
%o A155764         a += 1
%o A155764 m += 1 # _Ya-Ping Lu_, Nov 27 2020
%Y A155764 Cf. A155765 (where records occur in A047160).
%K A155764 nonn
%O A155764 1,3
%A A155764 _T. D. Noe_, Jan 27 2009