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A068700 The concatenation of n with n-1 and n with n+1 both yield primes (twin primes). 4

%I

%S 42,78,102,108,180,192,270,300,312,330,342,390,420,522,540,612,660,

%T 822,840,882,1002,1140,1230,1272,1482,1542,1632,1770,2100,2190,2682,

%U 2742,3072,3198,3408,3642,3828,4242,4452,4572,4740,4788,4998,5622,5718,5832

%N The concatenation of n with n-1 and n with n+1 both yield primes (twin primes).

%C All terms are congruent to {0, 12, 18} mod 30. - _Zak Seidov_, Oct 24 2014

%C a(n) = 2 * A102478(n). - _Reinhard Zumkeller_, Jun 27 2015

%H Zak Seidov, <a href="/A068700/b068700.txt">Table of n, a(n) for n = 1..10000</a>

%e 42 is a member as 4241 as well as 4243 are primes.

%p filter:= proc(n)

%p local d;

%p d:= ilog10(n)+1;

%p isprime(n*10^d+n-1) and isprime(n*10^d+n+1)

%p end proc:

%p select(filter, [$1..10^5]); # _Robert Israel_, Oct 24 2014

%t d[n_]:=IntegerDigits[n]; conQ[n_]:=And@@PrimeQ[FromDigits/@{Join[d[n],d[n+1]],Join[d[n],d[n-1]]}]; Select[Range[5850],conQ[#] &] (* _Jayanta Basu_, May 21 2013 *)

%o (PARI) for(n=2,200, if(isprime(n*10^ceil(log(n-1)/log(10))+n-1)*isprime(n*10^ceil(log(n+1)/log(10))+n+1)==1,print1(n,",")))

%o (Haskell)

%o import Data.List.Ordered (isect)

%o a068700 n = a068700_list !! (n-1)

%o a068700_list = isect a030457_list a054211_list

%o -- _Reinhard Zumkeller_, Jun 27 2015

%Y Common terms of A030458 and A052089.

%Y Intersection of A030457 and A054211; A102478.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Mar 04 2002

%E More terms from _Benoit Cloitre_, Mar 09 2002

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Last modified August 14 19:47 EDT 2020. Contains 336483 sequences. (Running on oeis4.)