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A032350 Palindromic nonprime numbers. 15


%S 1,4,6,8,9,22,33,44,55,66,77,88,99,111,121,141,161,171,202,212,222,

%T 232,242,252,262,272,282,292,303,323,333,343,363,393,404,414,424,434,

%U 444,454,464,474,484,494,505,515,525,535,545,555,565,575,585,595,606,616

%N Palindromic nonprime numbers.

%C Complement of A002385 (palindromic primes) with respect to A002113 (palindromic numbers). Union of A222724, A043047 (without number 2), A222726, A043039, A043040 (without number 5), A043041, A222728, A043043 and A222729. - Jaroslav Krizek, Mar 12 2013

%C Banks, Hart, and Sakata derive a nontrivial upper bound for the number of prime palindromes n <= x as x tends to infinity. It follows that almost all palindromes are composite. The results hold in any base. The authors use Weil's bound for Kloosterman sums. - _Jonathan Sondow_, Jan 02 2018

%H Jaroslav Krizek, <a href="/A032350/b032350.txt">Table of n, a(n) for n = 1..10217</a>

%H W. D. Banks, D. N. Hart, M. Sakata, <a href="http://dx.doi.org/10.4310/MRL.2004.v11.n6.a10">Almost all palindromes are composite</a>, Math. Res. Lett., 11 No. 5-6 (2004), 853-868.

%H P. De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a>

%H P. De Geest, <a href="http://www.worldofnumbers.com/palpri.htm">World!Of Palindromic Primes</a>

%t palq[n_] := IntegerDigits[n]==Reverse[IntegerDigits[n]]; Select[Range[700], palq[ # ]&&!PrimeQ[ # ]&]

%t (* Second program: *)

%t Select[Range@ 616, And[PalindromeQ@ #, ! PrimeQ@ #] &] (* _Michael De Vlieger_, Jan 02 2018 *)

%o (Sage)

%o [n for n in (1..616) if not is_prime(n) and Word(n.digits()).is_palindrome()] # _Peter Luschny_, Sep 13 2018

%o (GAP) Filtered([1..620],n-> not IsPrime(n) and ListOfDigits(n)=Reversed(ListOfDigits(n))); # _Muniru A Asiru_, Mar 08 2019

%Y Cf. A002385.

%K easy,nonn,base

%O 1,2

%A _Patrick De Geest_

%E Edited by _Dean Hickerson_, Oct 22 2002

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Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)