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Search: id:A093550
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| A093550 |
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a(n) is the smallest number m such that each of the numbers m-1, m and m+1 is a product of n distinct primes. |
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+0
6
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| 34, 1310, 203434, 16467034, 1990586014, 41704979954, 102099792179230
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Each term of this sequence is of the form 4k+2.
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LINKS
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Jacques Tramu, Puzzle 371
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FORMULA
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<< NumberTheory`NumberTheoryFunctions`; a[n_] := (For[m=1, !(Length[FactorInteger[4m+1]]==n && SquareFreeQ[4m+1] && Length[FactorInteger[4m+2]]==n && SquareFreeQ[4m+2] && Length[FactorInteger[4m+3]]==n && SquareFreeQ[4m+3]), m++ ]; 4m+2)
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EXAMPLE
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a(5)=16467034 because each of the three numbers 16467034-1, 16467034 & 16467034+1 are products of 5 distinct primes (16467033=3*11*17*149*197, 16467034=2*19*23*83*227, 16467035=5*13*37*41*167) and 16467034 is the smallest such number.
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MATHEMATICA
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<< NumberTheory`NumberTheoryFunctions`; a[n_] := (For[m=1, !(Length[FactorInteger[4m+1]]==n && SquareFreeQ[4m+1] && Length[FactorInteger[4m+2]]==n && SquareFreeQ[4m+2] && Length[FactorInteger[4m+3]]==n && SquareFreeQ[4m+3]), m++ ]; 4m+2); Do[Print[a[n]], {n, 2, 6}]
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CROSSREFS
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Cf. A093549, A052215, A093548.
Sequence in context: A041545 A167258 A158731 this_sequence A123790 A086881 A056566
Adjacent sequences: A093547 A093548 A093549 this_sequence A093551 A093552 A093553
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KEYWORD
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more,nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 07 2004, corrected Aug 26 2006; a(7) added from Jacques Tramu's web site, Aug 26 2006
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EXTENSIONS
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a(8) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 27 2008
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