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

20, 53, 341, 536, 2312, 2477, 3380, 3665, 3686, 4547, 5009, 5105, 6458, 6488, 6731, 6845, 7499, 7508, 7562, 7835, 8411, 8831, 9032, 9386, 9764, 9839, 11027, 11885, 14990, 19589, 20498, 21080, 22844, 24821, 25220, 26393, 27593, 29864, 29921

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Example

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

Mathematica

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} ] ] ] & ]
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 *)

Crossrefs

Cf. A032682, A059693, A059694.

Sequence in context: A329627 A329628 A302885 * A301372 A108108 A316935

Adjacent sequences: A059674 A059675 A059676 * A059678 A059679 A059680

Keyword

base,nonn

Author

Harvey P. Dale, Feb 05 2001

Extensions

More terms from Patrick De Geest, Feb 07 2001

Status

approved