

A140332


Products of two palindromes in base 10.


1



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 54, 55, 56, 63, 64, 66, 72, 77, 81, 88, 99, 101, 110, 111, 121, 131, 132, 141, 151, 154, 161, 165, 171, 176, 181, 191, 198
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OFFSET

1,3


COMMENTS

Genevieve Paquin, p. 5: "Lemma 3.7: a Christoffel word can always be written as the product of two palindromes." Products of two palindromes in base 10 may be either a palindrome (e.g., 202 * 202 = 40804} or a nonpalindrome (e.g., 2 * 88 = 176, or 22 * 33 = 726}. Contains A115683 as a proper subset. The nonpalindromes in this sequence are the same as the nonpalindromes in A115683: {10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72, 81, 110, 132, 154, 165, 176, 198, 220, 231, 264, 275, 297, 302, 308, 322, 330, ...} which is not yet a sequence in the OEIS.


LINKS

Table of n, a(n) for n=1..62.
Genevieve Paquin, On a generalization of Christoffel words: epichristoffel words, arXiv:0805.4174 [math.CO], 20082009.


FORMULA

{i*j such that i is in A002113 and j is in A002113} = A002113 UNION A115683.


MATHEMATICA

pal = Select[ Range[0, 200], # == FromDigits@ Reverse@ IntegerDigits@ # &]; Select[ Union[ Times @@@ Tuples[pal, 2]], # <= 200 &] (* Giovanni Resta, Jun 20 2016 *)


CROSSREFS

Cf. A002113, A115683.
Sequence in context: A084034 A084347 A051038 * A155182 A096076 A108864
Adjacent sequences: A140329 A140330 A140331 * A140333 A140334 A140335


KEYWORD

easy,nonn,base


AUTHOR

Jonathan Vos Post, May 28 2008


EXTENSIONS

Data corrected by Giovanni Resta, Jun 20 2016


STATUS

approved



