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A086505 a(n) is the n-th smallest prime p such that p+2n is also prime.

%I A086505 #18 Aug 07 2014 04:25:03
%S A086505 3,7,11,23,31,29,53,73,53,89,157,73,137,199,73,281,229,127,383,229,
%T A086505 149,389,463,193,359,547,239,467,823,197,857,883,283,809,499,389,1013,
%U A086505 907,421,827,1201,373,1151,1231,367,1307,1279,577,1229,1009,631,1427,1783
%N A086505 a(n) is the n-th smallest prime p such that p+2n is also prime.
%C A086505 Note the patterns in the graph. These patterns depend on the number of prime factors of n: see color graph for different n's: n primes - black dots, n multiples of 3 - red dots, n multiples of 15 - green dots, n multiples of 105 - blue dots. - _Zak Seidov_, Nov 28 2013
%H A086505 Zak Seidov, <a href="/A086505/b086505.txt">Table of n, a(n) for n = 1..10000</a>
%H A086505 Zak Seidov, <a href="/A086505/a086505.jpg">Color graph for different n's</a>
%p A086505 N:= 10^4: # to get all terms before the first with a(n)+2*n > N
%p A086505 Primes:= select(isprime, {seq(2*i+1, i=1..N)}):
%p A086505 for n from 1 do
%p A086505 R:= Primes intersect map(`+`, Primes, -2*n);
%p A086505 if nops(R) < n then break fi;
%p A086505 A[n]:= R[n];
%p A086505 od:
%p A086505 seq(A[j],j=1..n-1); # _Robert Israel_, Aug 07 2014
%Y A086505 Cf. A020483, A231608.
%K A086505 nonn
%O A086505 1,1
%A A086505 _Amarnath Murthy_, Jul 29 2003
%E A086505 Edited by _Sam Alexander_, Feb 26 2004