A117058 Palindromes for which the product of the digits is prime.

2, 3, 5, 7, 121, 131, 151, 171, 11211, 11311, 11511, 11711, 1112111, 1113111, 1115111, 1117111, 111121111, 111131111, 111151111, 111171111, 11111211111, 11111311111, 11111511111, 11111711111, 1111112111111, 1111113111111

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,110,-110,0,0,-1000,1000).

Formula

From Chai Wah Wu, Nov 13 2018: (Start)

a(n) = a(n-1) + 110*a(n-4) - 110*a(n-5) - 1000*a(n-8) + 1000*a(n-9) for n > 9.

G.f.: x*(-500*x^8 + 200*x^7 + 200*x^6 + 100*x^5 + 106*x^4 - 2*x^3 - 2*x^2 - x - 2)/((x - 1)*(10*x^2 - 1)*(10*x^2 + 1)*(10*x^4 - 1)). (End)

Example

11211 is in the sequence because it is a palindrome and the product of its digits 1*1*2*1*1=2 is a prime.

Mathematica

Sort[Flatten[Table[NestList[FromDigits[Flatten[{1, IntegerDigits[#], 1}]] &, n, 6], {n, Prime[Range[4]]}]]] (* Jayanta Basu, Jul 13 2013 *)
LinearRecurrence[{1, 0, 0, 110, -110, 0, 0, -1000, 1000}, {2, 3, 5, 7, 121, 131, 151, 171, 11211}, 40] (* Vincenzo Librandi, Nov 14 2018 *)

Prog

(PARI) isok(n) = my(d=digits(n)); (Vecrev(d) == d) && isprime(vecprod(d)); \\ Michel Marcus, Nov 14 2018
(Magma) I:=[2, 3, 5, 7, 121, 131, 151, 171, 11211]; [n le 9 select I[n] else Self(n-1)+110*Self(n-4)-110*Self(n-5)-1000*Self(n-8)+1000*Self(n-9): n in [1..30]]; // Vincenzo Librandi, Nov 14 2018

Crossrefs

Cf. A002113.

Sequence in context: A119835 A076609 A117059 * A067173 A357262 A340113

Adjacent sequences: A117055 A117056 A117057 * A117059 A117060 A117061

Keyword

base,easy,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006

Status

approved