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Search: id:A109287
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| A109287 |
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4-almost primes equal to p*q + 1, where p and q are (not necessarily distinct) primes. |
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+0
9
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| 16, 36, 40, 56, 88, 135, 156, 184, 204, 210, 220, 248, 250, 260, 296, 306, 315, 328, 330, 340, 342, 372, 414, 459, 472, 490, 516, 536, 546, 580, 584, 636, 650, 686, 690, 708, 714, 732, 735, 738, 804, 808, 819, 836, 850, 852, 870, 872, 940, 950, 966, 975, 996
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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4-almost primes of the form semiprime + 1.
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FORMULA
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a(n) is in this sequence iff a(n) is in A014613 and (a(n)-1) is in A001358.
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EXAMPLE
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a(1) = 16 because (3*5+1)=(2^4) = 16.
a(2) = 36 because (5*7+1)=((2^2)*(3^2)) = 36.
a(3) = 40 because (3*13+1)=((2^3)*5) = 40.
a(4) = 56 because (5*11+1)=((2^3)*7) = 56.
a(5) = 88 because (3*29+1)=((2^3)*11) = 88.
a(6) = 135 because (2*67+1)=((3^3)*5) = 135.
a(7) = 156 because (5*31+1)=((2^2)*3*13) = 156.
a(8) = 184 because (3*61+1)=((2^3)*23) = 184.
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MATHEMATICA
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bo[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[1000], bo[ # ] == 4 && bo[ # - 1] == 2 &] (*Chandler*)
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CROSSREFS
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Primes are in A000040. Semiprimes are in A001358. 4-almost primes are in A014613.
Primes of the form semiprime + 1 are in A005385 (safe primes).
Semiprimes of the form semiprime + 1 are in A109373.
3-almost primes of the form semiprime + 1 are in A109067.
4-almost primes of the form semiprime + 1 are in this sequence.
5-almost primes of the form semiprime + 1 are in A109383.
Least n-almost prime of the form semiprime + 1 are in A128665.
Similar to A076153; after A076153(0)=3 next difference is A076153(100)=1792 whereas A109287(100)=1794.
Cf. A077065, A079148, A092307, A109288, A109289, A109290.
Sequence in context: A086119 A105509 A070588 this_sequence A066112 A103843 A144548
Adjacent sequences: A109284 A109285 A109286 this_sequence A109288 A109289 A109290
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KEYWORD
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easy,nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it) and Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 20 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Aug 27 2005
Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 20 2007
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