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A156053 Let m = A002445(n); then a(n) = largest member of A001359 (the lesser twin primes sequence) <= m.

%I A156053 #4 May 01 2013 21:13:44
%S A156053 5,29,41,2729,137,14321,281,3404309,33329,641,4206929,1366529,281189,
%T A156053 7589,625169,5009,2081,63029,5477,2657,2801,15269,19469,25997,49169,
%U A156053 11489,23909,289109,14009,129629,32909,3254729,88577309,93809,412589
%N A156053 Let m = A002445(n); then a(n) = largest member of A001359 (the lesser twin primes sequence) <= m.
%H A156053 Wikimedia Commons, <a href="http://commons.wikimedia.org/wiki/File:OEIS_A156053.svg">Alternate plot</a>
%o A156053 (PARI) \\ uses Pari functions ispseudoprime, denominator, and list \\ tp2cnt =count of adjacent, unique twin primes (lower) \\ p2cnt = count of unique adjacent primes \\ N = Bernoulli # maxx= max N idx*=list pointers \\ u=array of adj. unique TP u2=array of adj. unique primes cnt=0;pcnt=0;n=1;opcnt=0;plcnt=0;phcnt=0;tpcnt=0;otpcnt=0; tp2cnt=0;p2cnt=0; limmit=429000001; \\4E8 idx=1; \\init idx2=1;
%o A156053 \\init if(maxx<2,maxx=2); if(maxx>200000,maxx=200000); print ("enforced n max = ",maxx); u=listcreate(500); \\unique entries < 10% TP u2=listcreate(5000); \\unique entries < 50% while(n<maxx+1, if(bernfrac(n)==0,n++) ; \\guard against 0 division m=abs(denominator(bernfrac(n)) ); p=m-1;q=m+1;
%o A156053 \\ we check to either side cnt++; if( ispseudoprime(p)==1, plcnt++ ); if( ispseudoprime(q)==1, phcnt++ ); if( ispseudoprime(q)==1 || ispseudoprime(p)==1, pcnt++ ); if( ispseudoprime(q)==1 && ispseudoprime(p)==1, tpcnt++ ); if( tpcnt>otpcnt, print("TP! @ ",n," ",q, " "
%o A156053 \\IF.FOR,IF if(p>0,listput(u,p,idx);tp2cnt++ ); if(p>0,idx++) ); \\ end IF if( pcnt>opcnt, if(p>limmit,p=0); \\lower if(ispseudoprime(p)==0,p=0); if(p>0, for(z=1,idx2-1, if(p==u2[z],p=0); ); ); if(p>0,listput(u2,p,idx2);p2cnt++); if(p>0,idx2++); if(q>limmit,q=0);
%o A156053 \\upper if(ispseudoprime(q)==0,q=0); if(q>0, for(z=1,idx2-1, if(q==u2[z],q=0); ); ); if(q>0,listput(u2,q,idx2);p2cnt++); if(q>0,idx2++) ); \\ end IF opcnt=pcnt;otpcnt=tpcnt; n++ ); \\end WHILE if(cnt>0, print(2.*p2cnt/cnt) ); \\reflect every other (n.z.) print ("TP count = ",tp2cnt ); print ("enforced n max = ",maxx);
%Y A156053 Cf. A002445
%K A156053 easy,nonn
%O A156053 1,1
%A A156053 _Bill McEachen_, Feb 02 2009
%E A156053 Edited by _N. J. A. Sloane_, Oct 21 2009