A347279 - OEIS

A347279

First member p(m) of the m-th twin prime pair such that d(m) < 0 and d(m-1) > 0, with d(k) = k/Integral_{x=2..p(k)} 1/log(x)^2 dx - C, C = 2*A005597 = A114907.

%I #8 Aug 30 2021 17:18:25

%S 1371911,1372757,1393919,1417991,1425881,1428671,1429247,1429859,

%T 1430711,1495379,1502687,1503317,1510217,35278601,35280029,35446781,

%U 35463497,35468789,35469779,35472137,45225161,45274751,45276689,45306641,45324551,45336407,45336761,45337517

%N First member p(m) of the m-th twin prime pair such that d(m) < 0 and d(m-1) > 0, with d(k) = k/Integral_{x=2..p(k)} 1/log(x)^2 dx - C, C = 2*A005597 = A114907.

%C See A347278 for more information.

%H Hugo Pfoertner, <a href="/A347279/b347279.txt">Table of n, a(n) for n = 1..12134</a>

%F A347278(n) < a(n) < A347278(n+1).

%o (PARI) \\ see A347278 for auxiliary functions halicon and Li.

%o a347279(nterms,CHL) = {my(n=2,pprev=1,np=0);

%o forprime(p=11,, if(p%6!=1&&ispseudoprime(p+2), n++; L=Li(2,p); my(x=n/L-CHL); if(x*pprev>0, if(pprev<0,print1(p,", "); np++; if(np>nterms,return)); pprev=-pprev)))};

%o a347279(10, halicon([0,2]))

%Y Cf. A001359, A005597, A114907, A347278.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Aug 26 2021