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A083966
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Numbers n such that the concatenation 2n3n5n7 is prime.
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5
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1, 6, 8, 9, 16, 17, 18, 21, 23, 24, 29, 32, 39, 64, 70, 78, 84, 85, 98, 1000, 1005, 1013, 1033, 1038, 1041, 1047, 1056, 1065, 1066, 1076, 1087, 1091, 1102, 1107, 1109, 1115, 1118, 1121, 1137, 1139, 1152, 1156, 1164, 1167, 1171, 1173, 1185, 1199, 1220, 1241
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OFFSET
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1,2
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COMMENTS
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Numbers n such that the concatenation of 2, n, 3, n, 5, n and 7 is prime.
This concatenation is fp(4, n) as defined in A083677.
For any 3-digit number n, fp(4, n) is divisible by 7, so there are no 3-digit numbers in the sequence.
More generally, there are no (3+6*k)-digit numbers in the sequence for any k. - Robert Israel, Nov 12 2019
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LINKS
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EXAMPLE
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8 and 21 are in the sequence because 2838587 and 2213215217 are primes.
16 is in the sequence because 2163165167 is prime.
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MAPLE
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filter:= proc(n) local m;
m:= ilog10(n)+1;
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))
end proc:
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MATHEMATICA
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v={}; Do[If[PrimeQ[FromDigits[Join[{2}, IntegerDigits[n], {3}, IntegerDigits[n], {5}, IntegerDigits[n], {7}]]], v=Append[v, n]], {n, 1300}]; v
Select[Range[1300], PrimeQ[FromDigits[Flatten[IntegerDigits/@ Riffle[ {2, 3, 5, 7}, Table[#, {3}]]]]]&](* Harvey P. Dale, Nov 24 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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