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A068700

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

42, 78, 102, 108, 180, 192, 270, 300, 312, 330, 342, 390, 420, 522, 540, 612, 660, 822, 840, 882, 1002, 1140, 1230, 1272, 1482, 1542, 1632, 1770, 2100, 2190, 2682, 2742, 3072, 3198, 3408, 3642, 3828, 4242, 4452, 4572, 4740, 4788, 4998, 5622, 5718, 5832

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All terms are congruent to {0, 12, 18} mod 30. - Zak Seidov, Oct 24 2014

a(n) = 2 * A102478(n). - Reinhard Zumkeller, Jun 27 2015

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

EXAMPLE

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

MAPLE

filter:= proc(n)

local d;

d:= ilog10(n)+1;

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

end proc:

select(filter, [$1..10^5]); # Robert Israel, Oct 24 2014

MATHEMATICA

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 *)

PROG

(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, ", ")))

(Haskell)

import Data.List.Ordered (isect)

a068700 n = a068700_list !! (n-1)

a068700_list = isect a030457_list a054211_list

-- Reinhard Zumkeller, Jun 27 2015

CROSSREFS

Common terms of A030458 and A052089.

Intersection of A030457 and A054211; A102478.

Sequence in context: A259737 A039525 A072326 * A303283 A135850 A250381

Adjacent sequences: A068697 A068698 A068699 * A068701 A068702 A068703