A117058 - OEIS

%I #16 Sep 08 2022 08:45:24

%S 2,3,5,7,121,131,151,171,11211,11311,11511,11711,1112111,1113111,

%T 1115111,1117111,111121111,111131111,111151111,111171111,11111211111,

%U 11111311111,11111511111,11111711111,1111112111111,1111113111111

%N Palindromes for which the product of the digits is prime.

%H Vincenzo Librandi, <a href="/A117058/b117058.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,110,-110,0,0,-1000,1000).

%F From _Chai Wah Wu_, Nov 13 2018: (Start)

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

%F 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)

%e 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.

%t Sort[Flatten[Table[NestList[FromDigits[Flatten[{1, IntegerDigits[#], 1}]] &, n, 6], {n, Prime[Range[4]]}]]] (* _Jayanta Basu_, Jul 13 2013 *)

%t 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 *)

%o (PARI) isok(n) = my(d=digits(n)); (Vecrev(d) == d) && isprime(vecprod(d)); \\ _Michel Marcus_, Nov 14 2018

%o (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

%Y Cf. A002113.

%K base,easy,nonn

%O 1,1

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