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A161721 Primes p such that the reversal of p is prime and the product of p with its reversal is a palindrome. 2
2, 3, 11, 101, 1021, 1201, 111211, 112111, 1000211, 1010201, 1020101, 1101211, 1102111, 1111021, 1112011, 1120001, 1121011, 1201111, 10011101, 10012001, 10021001, 10100201, 10111001, 10200101, 11012011, 11021011, 11100121, 12100111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is a subsequence of A062936. If you multiply a member of this sequence by its reversal you get a number fixed under TITO algorithm (see A161594).

Conjecture: except for a(2) which equals 3, all terms can only be composed of the digits 0, 1 or 2. - Chai Wah Wu, Jan 07 2015

Conjecture: the digit 2 can only appear once in each term. - Robert G. Wilson v, Jan 07 2015

Number of terms less than 10^n: 2, 3, 4, 6, 6, 8, 18, 28, 37, 65, 97, 153, 230, 304, 414, 556, 756, 960, 1255, ... - Robert G. Wilson v, Jan 07 2015

A proper subset of A007500. - Robert G. Wilson v, Jan 07 2015

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..1255 (first 97 terms from Chai Wah Wu)

T. Khovanova, Turning Numbers Inside Out [From Tanya Khovanova, Jul 07 2009]

EXAMPLE

1021 is a prime number, its reversal is 1201, which is also a prime. The product 1021*1201 = 1226221 is a palindrome.

MAPLE

rev := proc (n) local nn: nn := convert(n, base, 10): add(nn[j]*10^(nops(nn)-j), j = 1 .. nops(nn)) end proc: a := proc (n) local p: p := ithprime(n): if isprime(rev(p)) = true and rev(p*rev(p)) = p*rev(p) then p else end if end proc: seq(a(n), n = 1 .. 800000); # Emeric Deutsch, Jun 26 2009

MATHEMATICA

rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; t={}; Do[p=Prime[n]; If[PrimeQ[q=rev[p]] && rev[p*q]==p*q, AppendTo[t, p]], {n, 8*10^5}]; t (* Jayanta Basu, May 11 2013 *)

PROG

(Python)

from sympy import isprime

A161721_list = [2]

for i in range(3, 10**6, 2):

....j = int(str(i)[::-1])

....if j == i:

........s = str(i**2)

........if s == s[::-1] and isprime(i):

............A161721_list.append(i)

....elif j > i:

........s = str(i*j)

........if s == s[::-1] and isprime(i) and isprime(j):

............A161721_list.extend([i, j])

A161721_list = sorted(A161721_list) # Chai Wah Wu, Jan 07 2015

CROSSREFS

Cf. A161594, A161597, A161600.

Sequence in context: A056899 A117699 A065378 * A225603 A292710 A300898

Adjacent sequences:  A161718 A161719 A161720 * A161722 A161723 A161724

KEYWORD

base,nonn

AUTHOR

Tanya Khovanova, Jun 17 2009

EXTENSIONS

Edited by N. J. A. Sloane, Jun 23 2009

More terms from Emeric Deutsch, Jun 26 2009

STATUS

approved

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Last modified August 7 11:08 EDT 2020. Contains 336275 sequences. (Running on oeis4.)