A117825 - OEIS

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A117825

Distance from n-th highly composite number (cf. A002182) to nearest prime.

1, 0, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 11, 13, 1, 11, 1, 17, 1, 1, 13, 13, 1, 1, 17, 1, 17, 1, 1, 17, 17, 17, 1, 1, 19, 37, 37, 1, 17, 23, 1, 29, 1, 1, 19, 1, 19, 23, 1, 19, 31, 1, 19, 1, 1, 1, 1, 23, 1, 29, 23, 23, 1, 23, 71, 37, 1, 1, 31, 1, 23, 53, 1, 31 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,10`
	COMMENTS	`a) Conjecture: entries > 1 will always be prime. The entry will be larger than the largest prime factor of the highly composite number.` `b) Will 1 always be the most common entry?` `c) While a prime may always located close to each highly composite number, is the converse false?` `d) Is there always a prime between successive highly composite numbers?`
	LINKS	`Charles Greathouse IV, Table of n, a(n) for n = 1..19999` `Graeme McRae, Highly Composite Numbers` `Wikipedia, Highly Composite Numbers.` `Wikipedia, Divisor Function (sigma).` `Wikimedia Commons,Alternate plot`
	EXAMPLE	`a(5) = abs(12-11)=1.`
	CROSSREFS	`Sequence in context: A074465 A081229 A109010 * A010143 A101027 A129408` `Adjacent sequences: A117822 A117823 A117824 * A117826 A117827 A117828`
	KEYWORD	`nonn`
	AUTHOR	`Bill McEachen, May 01 2006`
	EXTENSIONS	`More terms from Don Reble (djr(AT)nk.ca), May 02 2006`

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Last modified February 17 03:45 EST 2012. Contains 205978 sequences.