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A115186 Smallest number m such that m and m+1 have exactly n prime factors (counted with multiplicity). 15
2, 9, 27, 135, 944, 5264, 29888, 50624, 203391, 3290624, 6082047, 32535999, 326481920, 3274208000, 6929459199, 72523096064, 37694578688, 471672487935, 11557226700800, 54386217385983, 50624737509375, 275892612890624, 4870020829413375, 68091093855502335, 2280241934368767 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A001222(a(n)) = A001222(a(n)+1) = n: subsequence of A045920.
a(16) > 4*10^10. - Martin Fuller, Jan 17 2006
a(n) <= A093548(n) <= A052215(n). - Zak Seidov, Jan 16 2015
Apparently, 4*a(n)+2 is the least number k such that k-2 and k+2 have exactly n+2 prime factors, counted with multiplicity. - Hugo Pfoertner, Apr 02 2024
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 135, p. 46, Ellipses, Paris 2008.
LINKS
EXAMPLE
a(10) = 3290624 = 6427 * 2^9, 3290624+1 = 13 * 5^5 * 3^4:
A001222(3290624) = A001222(3290625) = 10.
CROSSREFS
Equivalent sequences for longer runs: A113752 (3), A356893 (4).
Sequence in context: A123904 A327612 A019065 * A243560 A090900 A357721
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 16 2006
EXTENSIONS
a(13)-a(15) from Martin Fuller, Jan 17 2006
a(16)-a(17) from Donovan Johnson, Apr 08 2008
a(18)-a(22) from Donovan Johnson, Jan 21 2009
a(23)-a(25) from Donovan Johnson, May 25 2013
STATUS
approved

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Last modified May 23 16:36 EDT 2024. Contains 372765 sequences. (Running on oeis4.)