A169916 - OEIS

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A169916

Squares in carryless arithmetic mod 10 with addition and multiplication of digits both defined to be addition mod 10.

0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 220, 242, 264, 286, 208, 220, 242, 264, 286, 208, 440, 462, 484, 406, 428, 440, 462, 484, 406, 428, 660, 682, 604, 626, 648, 660, 682, 604, 626, 648, 880, 802, 824, 846, 868, 880, 802, 824, 846, 868, 0, 22, 44, 66, 88, 0, 22, 44, 66, 88, 220, 242 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`The rules of arithmetic used in A169916, A169917, A169918 have very strange consequences. Many of the familiar laws fail. For instance, the arithmetic in A169916 is not associative: 10(92) = 101 = 21 != (109)2 = 92 = 1.`
	LINKS	`Table of n, a(n) for n=0..61.` `Index entries for sequences related to carryless arithmetic`
	EXAMPLE	`a(16) = 1616 = 242:` `....16` `....16` `------` `....72 (66 = 6+6 mod 10 = 2, 6*1 = 6+1 mod 10 = 7)` `...27.` `------` `...242` `------`
	CROSSREFS	`The four versions are A059729, A169916, A169917, A169918.` `Sequence in context: A113603 A004520 A169918 * A073909 A036211 A127353` `Adjacent sequences: A169913 A169914 A169915 * A169917 A169918 A169919`
	KEYWORD	`nonn,base`
	AUTHOR	`David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 20 2010`
	STATUS	`approved`

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Last modified May 20 10:38 EDT 2013. Contains 225458 sequences.