Editing Palindromic number (section)

==Scheherazade numbers==
'''Scheherazade numbers''' are a set of numbers identified by [[Buckminster Fuller]] in his book ''Synergetics''.<ref>R. Buckminster Fuller, with E. J. Applewhite, [http://www.rwgrayprojects.com/synergetics/s12/p2200.html#1230.00 ''Synergetics: Explorations in the Geometry of thinking''] {{Webarchive|url=https://web.archive.org/web/20160227163051/http://www.rwgrayprojects.com/synergetics/s12/p2200.html#1230.00 |date=2016-02-27 }}, Macmillan, 1982 {{ISBN|0-02-065320-4}}.</ref>  Fuller does not give a formal definition for this term, but from the examples he gives, it can be understood to be those numbers that contain a factor of the [[primorial]] ''n''#, where ''n''≥13 and is the largest [[prime factor]] in the number.  Fuller called these numbers ''Scheherazade numbers'' because they must have a factor of 1001.  [[Scheherazade]] is the storyteller of ''[[One Thousand and One Nights]]'', telling a new story each night to delay her execution.  Since ''n'' must be at least 13, the primorial must be at least 1·2·3·5·7·11·13, and 7×11×13 = 1001.  Fuller also refers to powers of 1001 as Scheherazade numbers.  The smallest primorial containing Scheherazade number is 13# = 30,030.

Fuller pointed out that some of these numbers are palindromic by groups of digits.  For instance 17# = 510,510 shows a symmetry of groups of three digits.  Fuller called such numbers ''Scheherazade Sublimely Rememberable Comprehensive Dividends'', or SSRCD numbers.  Fuller notes that 1001 raised to a power not only produces ''sublimely rememberable'' numbers that are palindromic in three-digit groups, but also the values of the groups are the [[binomial coefficient]]s. For instance,
:<math>(1001)^6 = 1,006,015,020,015,006,001 </math>

This sequence fails at (1001)<sup>13</sup> because there is a [[Carry (arithmetic)|carry digit]] taken into the group to the left in some groups.  Fuller suggests writing these ''spillovers'' on a separate line.  If this is done, using more spillover lines as necessary, the symmetry is preserved indefinitely to any power.<ref>Fuller, [http://www.rwgrayprojects.com/synergetics/s12/p3100.html pp. 773-774] {{Webarchive|url=https://web.archive.org/web/20160305202829/http://www.rwgrayprojects.com/synergetics/s12/p3100.html |date=2016-03-05 }}</ref>  Many other Scheherazade numbers show similar symmetries when expressed in this way.<ref>Fuller, pp. 777-780</ref>