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

Author

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

Keywords

• base
• easy
• nonn

Examples

			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.
		

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).

Crossrefs

Cf. A002113.

Programs

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

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 *)

PARI

isok(n) = my(d=digits(n)); (Vecrev(d) == d) && isprime(vecprod(d)); \\ Michel Marcus, Nov 14 2018

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)