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A083966 Numbers n such that the concatenation 2n3n5n7 is prime.

%I A083966 #25 Nov 12 2019 23:44:52
%S A083966 1,6,8,9,16,17,18,21,23,24,29,32,39,64,70,78,84,85,98,1000,1005,1013,
%T A083966 1033,1038,1041,1047,1056,1065,1066,1076,1087,1091,1102,1107,1109,
%U A083966 1115,1118,1121,1137,1139,1152,1156,1164,1167,1171,1173,1185,1199,1220,1241
%N A083966 Numbers n such that the concatenation 2n3n5n7 is prime.
%C A083966 Numbers n such that the concatenation of 2, n, 3, n, 5, n and 7 is prime.
%C A083966 This concatenation is fp(4, n) as defined in A083677.
%C A083966 For any 3-digit number n, fp(4, n) is divisible by 7, so there are no 3-digit numbers in the sequence.
%C A083966 More generally, there are no (3+6*k)-digit numbers in the sequence for any k. - _Robert Israel_, Nov 12 2019
%H A083966 Robert Israel, <a href="/A083966/b083966.txt">Table of n, a(n) for n = 1..10000</a>
%e A083966 8 and 21 are in the sequence because 2838587 and 2213215217 are primes.
%e A083966 16 is in the sequence because 2163165167 is prime.
%p A083966 filter:= proc(n) local m;
%p A083966   m:= ilog10(n)+1;
%p A083966 isprime(n*(10 + 10^(m+2)+ 10^(2*m+3))+7+5*10^(m+1)+3*10^(2*m+2)+2*10^(3*m+3))
%p A083966 end proc:
%p A083966 select(filter, [$1..2000]); # _Robert Israel_, Nov 12 2019
%t A083966 v={};Do[If[PrimeQ[FromDigits[Join[{2},IntegerDigits[n],{3}, IntegerDigits[n],{5},IntegerDigits[n],{7}]]],v=Append[v,n]], {n,1300}];v
%t A083966 Select[Range[1300],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Riffle[ {2,3,5,7}, Table[#,{3}]]]]]&](* _Harvey P. Dale_, Nov 24 2015 *)
%o A083966 (PARI) is(n)=isprime(eval(Str(2,n,3,n,5,n,7))) \\ _Charles R Greathouse IV_, May 15 2013
%Y A083966 Cf. A032711, A083677, A083969, A092117.
%K A083966 base,easy,nonn
%O A083966 1,2
%A A083966 _Farideh Firoozbakht_, Jun 15 2003, Jun 19 2003
%E A083966 Edited and extended by _David Wasserman_, Dec 06 2004
%E A083966 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 31 2007