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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
Sequence in context: A347402 A117699 A065378 * A225603 A292710 A300898
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 June 24 10:07 EDT 2024. Contains 373674 sequences. (Running on oeis4.)