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A195104 Smallest prime p such that p*t(n) +- 1 is a twin prime pair, where t(n)=A014574(n) is the n-th twin prime average.

%I A195104 #26 Mar 07 2021 18:44:17
%S A195104 3,2,5,11,2,11,3,29,101,199,29,7,13,11,29,71,13,3,71,101,29,43,79,5,
%T A195104 11,11,5,29,61,2,2,11,19,11,29,5,11,7,41,19,181,19,59,5,11,7,29,11,41,
%U A195104 179,41,13,61,181,19,241,139,331,271,3,59,5,41,89,19,2,5,131,59,5,5,509,2
%N A195104 Smallest prime p such that p*t(n) +- 1 is a twin prime pair, where t(n)=A014574(n) is the n-th twin prime average.
%C A195104 a(n) = 2 for n in A158866. - _Robert Israel_, Mar 07 2021
%H A195104 Robert Israel, <a href="/A195104/b195104.txt">Table of n, a(n) for n = 1..10000</a>
%e A195104 a(4)=11 because 11*A014574(4) +- 1 = 11*18 +- 1 = 198 +- 1 is a twin prime pair, A014574(4) +- 1 = 18 +- 1 is also a twin prime pair, and 11 is prime.
%p A195104 A195104 := proc(n)
%p A195104     k := A014574(n) ;
%p A195104     for i from 1 do
%p A195104         p := ithprime(i) ;
%p A195104         if isprime(p*k-1) and isprime(p*k+1) then
%p A195104             return p;
%p A195104         end if;
%p A195104     end do:
%p A195104 end proc:
%p A195104 seq(A195104(n),n=1..60) ; # _R. J. Mathar_, Dec 16 2011
%Y A195104 Cf. A014574, A158866.
%K A195104 nonn
%O A195104 1,1
%A A195104 _Juri-Stepan Gerasimov_, Dec 16 2011
%E A195104 a(64) corrected by _Robert Israel_, Mar 07 2021