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Search: id:A141554
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| A141554 |
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Transformed nonprime products of prime factors of the composites, the largest prime decremented by 2 and the smallest prime incremented by 2. |
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+0
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| 0, 4, 0, 12, 8, 20, 15, 0, 12, 24, 25, 36, 16, 21, 44, 15, 40, 36, 0, 45, 60, 35, 24, 68, 55, 48, 60, 72, 45, 84, 32, 45, 60, 75, 88, 36, 63, 80, 85, 108, 72, 116, 75, 0, 77, 108, 120, 105, 100, 48, 140, 75, 136, 81, 132, 96, 45, 156, 120, 105, 164, 135, 144, 108, 99, 168
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In the prime number decomposition of k=A002808(i), i=1,2,3,.., one instance of the largest prime, pmax=A052369(i), is replaced by pmax-2 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin+2. If the product of this modified list of factors, k*(pmax-2)*(pmin+2)/(pmin*pmax), is nonprime, it is added to the sequence.
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EXAMPLE
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k(1)=4=(p(max)=2)*(p(min)=2), transformed (2-2)*(2+2)=0*4=0=a(1).
k(2)=6=(p(max)=3)*(p(min)=2), transformed (3-2)*(2+2)=1*4=4=a(2).
k(3)=8=(p(max)=2)*(p=2)*(p(min)=2), transformed (2-2)*2*(2+2)=0*2*4=0=a(3).
k(4)=9=(p(max)=3)*(p(min)=3), transformed (3-2)*(3+2)=1*5=5 (prime, skipped).
k(5)=10=(p(max)=5)*(p(min)=2), transformed (5-2)*(2+2)=3*4=12=a(4).
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CROSSREFS
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Cf. A141218, A141219, A141220, A141284.
Sequence in context: A147607 A072194 A151921 this_sequence A076600 A002978 A056460
Adjacent sequences: A141551 A141552 A141553 this_sequence A141555 A141556 A141557
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 14 2008
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EXTENSIONS
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Edited and corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 18 2008
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