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A083966
Numbers n such that the concatenation 2n3n5n7 is prime.
5
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
OFFSET
1,2
COMMENTS
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
LINKS
EXAMPLE
8 and 21 are in the sequence because 2838587 and 2213215217 are primes.
16 is in the sequence because 2163165167 is prime.
MAPLE
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:
select(filter, [$1..2000]); # Robert Israel, Nov 12 2019
MATHEMATICA
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 *)
PROG
(PARI) is(n)=isprime(eval(Str(2, n, 3, n, 5, n, 7))) \\ Charles R Greathouse IV, May 15 2013
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Farideh Firoozbakht, Jun 15 2003, Jun 19 2003
EXTENSIONS
Edited and extended by David Wasserman, Dec 06 2004
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007
STATUS
approved