A032350 Palindromic nonprime numbers.

1, 4, 6, 8, 9, 22, 33, 44, 55, 66, 77, 88, 99, 111, 121, 141, 161, 171, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 323, 333, 343, 363, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565, 575, 585, 595, 606, 616

Offset: 1

Author

Patrick De Geest

Keywords

• easy
• nonn
• base

Comments

Complement of A002385 (palindromic primes) with respect to A002113 (palindromic numbers). - Jaroslav Krizek, Mar 12 2013

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

Links

• Georg Fischer, Table of n, a(n) for n = 1..10217
• W. D. Banks, D. N. Hart, and M. Sakata, Almost all palindromes are composite, Math. Res. Lett., 11 No. 5-6 (2004), 853-868.
• Patrick De Geest, World!Of Numbers
• Patrick De Geest, World!Of Palindromic Primes

Crossrefs

Cf. A002113, A002385.

Programs

GAP

Filtered([1..620],n-> not IsPrime(n) and ListOfDigits(n)=Reversed(ListOfDigits(n))); # Muniru A Asiru, Mar 08 2019

Mathematica

palq[n_] := IntegerDigits[n]==Reverse[IntegerDigits[n]]; Select[Range[700], palq[ # ]&&!PrimeQ[ # ]&]
(* Second program: *)
Select[Range@ 616, And[PalindromeQ@ #, ! PrimeQ@ #] &] (* Michael De Vlieger, Jan 02 2018 *)

Sage

[n for n in (1..616) if not is_prime(n) and Word(n.digits()).is_palindrome()] # Peter Luschny, Sep 13 2018

Extensions

Edited by Dean Hickerson, Oct 22 2002