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A117058 Palindromes for which the product of the digits is prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A340113 A090718

Adjacent sequences:  A117055 A117056 A117057 * A117059 A117060 A117061

KEYWORD

base,easy,nonn

AUTHOR

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

STATUS

approved

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Last modified December 3 18:19 EST 2021. Contains 349467 sequences. (Running on oeis4.)