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%I #7 Oct 01 2013 17:58:10
%S 29,53,92,126,204,281,333,489,573,816,1169,1585,1885,13906,24059,
%T 44421,48142,53394,84043,474045,489910,535841,2135727,3095936,3925702,
%U 4858924,6618689,8537111,58246902,163424560,188474341,193910248,785107460,847979055,6040627719,7900840637
%N Indices n of primes p(n), p(n+3) such that p(n)+1 and p(n+3)+1 have the same largest prime factor.
%C No other term <=210000. - _Emeric Deutsch_, Feb 13 2006
%p with(numtheory): a:=proc(n) local a, b: a:=factorset(1+ithprime(n)): b:=factorset(1+ithprime(n+3)): if a[nops(a)]=b[nops(b)] then n else fi end: seq(a(n),n=1..10000); # it takes hours - _Emeric Deutsch_, Feb 13 2006
%o (PARI) \prime indices such that gd of prime(x)+ k and prime(x+m) + k are equal divpm1(n,m,k) = { local(x,l1,l2,v1,v2); for(x=2,n, v1 = ifactor(prime(x)+ k); v2 = ifactor(prime(x+m)+k); l1 = length(v1); l2 = length(v2); if(v1[l1] == v2[l2], print1(x",") ) ) } ifactor(n) = \Vector of the prime factors of n { local(f,j,k,flist); flist=[]; f=Vec(factor(n)); for(j=1,length(f[1]), for(k = 1,f[2][j],flist = concat(flist,f[1][j]) ); ); return(flist) }
%K nonn
%O 2,1
%A _Cino Hilliard_, May 01 2005
%E One more term from _Emeric Deutsch_, Feb 13 2006
%E a(21)-a(37) from _Donovan Johnson_, Apr 03 2008