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

1,2

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

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 *)

Prog

(Sage)
[n for n in (1..616) if not is_prime(n) and Word(n.digits()).is_palindrome()] # Peter Luschny, Sep 13 2018
(GAP) Filtered([1..620], n-> not IsPrime(n) and ListOfDigits(n)=Reversed(ListOfDigits(n))); # Muniru A Asiru, Mar 08 2019

Crossrefs

Cf. A002113, A002385.

Sequence in context: A162738 A366826 A161600 * A078337 A046351 A161732

Adjacent sequences: A032347 A032348 A032349 * A032351 A032352 A032353

Keyword

easy,nonn,base

Author

Patrick De Geest

Extensions

Edited by Dean Hickerson, Oct 22 2002

Status

approved