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A059677 Numbers n such that 1n1, 3n3, 7n7 and 9n9 are all primes. 2

%I

%S 20,53,341,536,2312,2477,3380,3665,3686,4547,5009,5105,6458,6488,6731,

%T 6845,7499,7508,7562,7835,8411,8831,9032,9386,9764,9839,11027,11885,

%U 14990,19589,20498,21080,22844,24821,25220,26393,27593,29864,29921

%N Numbers n such that 1n1, 3n3, 7n7 and 9n9 are all primes.

%e 2312 is a term because 123121, 323123, 723127 and 923129 are all primes.

%t Select[ Range[ 30000 ], PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "1", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "3", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "7", {1, -1} ] ] ] && PrimeQ[ ToExpression[ StringInsert[ ToString[ # ], "9", {1, -1} ] ] ] & ]

%t enclose[n_]:=Table[FromDigits[Join[{i},IntegerDigits[n],{i}]],{i, {1,3,7,9}}]; Select[Range[30000],AllTrue[enclose[#],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 21 2015 *)

%Y Cf. A032682, A059693, A059694.

%K base,nonn

%O 1,1

%A _Harvey P. Dale_, Feb 05 2001

%E More terms from _Patrick De Geest_, Feb 07 2001

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Last modified September 26 23:32 EDT 2020. Contains 337378 sequences. (Running on oeis4.)