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A093548
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a(n) is the smallest number m such that each of the numbers m and m+1 has n distinct prime divisors.
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5
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2, 14, 230, 7314, 254540, 11243154, 965009045, 65893166030, 5702759516090, 490005293940084, 76622240600506314
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 2^63 < a(12) <= 22593106657425552170. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 08 2009]
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 230, p. 65, Ellipses, Paris 2008.
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FORMULA
| a[n_] := (For[m=1, !(Length[FactorInteger[m]]==n && Length[FactorInteger[m+1]]==n), m++ ];m)
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EXAMPLE
| a(5) =254540 because 254540=2^2*5*11*13*89; 254541=3*7*17*23*31
and 254540 is the smallest number m which each of the numbers m & m+1 has 5 distinct prime divisors.
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MATHEMATICA
| a[n_] := (For[m=1, !(Length[FactorInteger[m]]==n && Length[FactorInteger[m+1]]==n), m++ ]; m); Do[Print[a[n]], {n, 7}]
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CROSSREFS
| Cf. A052215, A093549, A093550, A115186.
Sequence in context: A105749 A118086 A048163 * A052215 A053846 A053855
Adjacent sequences: A093545 A093546 A093547 * A093549 A093550 A093551
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KEYWORD
| nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 06 2004
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EXTENSIONS
| a(8), a(9) from Martin Fuller (martin_n_fuller(AT)btinternet.com), Jan 17 2006
a(10)-a(11) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 08 2009
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