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Search: id:A084931
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| A084931 |
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Consider trajectory of n under repeated applications of the function f(x) = 'Sum of the prime factors of x (with multiplicity)' (see A029908). Sequence gives composite numbers n that end at a prime m that divides n, and m is greater than any m's seen already. |
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+0
2
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| 15, 21, 182, 494, 1219, 2852, 3182, 9782, 19339, 19982, 22454, 72836, 76814, 102134, 156782, 192182, 423182, 750979, 758894, 1364534, 1465454, 1548782, 2376182, 3379982, 4066934, 4204982
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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With a prime triple (p,p+4,p+6), the number a(n) = 2*p*(p+6) is always in the sequence, f( f( 2*p*(p+6) )) = f( 2*(p+4) ) = p+6. Such prime triples can be found in sequence A022005.
As long as two successive triples (p1,p1 + 4,p1 + 6) and (p2,p2 + 4,p2 + 6) of A022005 have p2 < 1.2*p1, no other numbers occur in the sequence between a(n1) and a(n2), this holds at least for larger p1 > 500. Other types of prime sets occurring in the sequence: (p,p+4,3p-4) with F( F( (p+4)*(3p-4))) = F( 4p ) = p + 4 (p,p+6,p+8) with F( F( 4*p*(p+8) )) = F( 2*(p+6) ) = p + 8.
Large examples of (p,p+4,++6)-triples: (108748629354*4436*3251#*(4436*3251#+1)+210)*(4436*3251#-1)/35 + 7, + 11, + 13 (4135 digits, David Broadhurst) (18599651274*4436*3251#*(4436*3251#+1)+210)*(4436*3251#-1)/35 + 7, + 11, +13 (4134 digits, David Broadhurst) Record examples of prime triples can be found on Tony Forbes's web site. There are triples of type (p,p+4,p+6) too.
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EXAMPLE
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a(10) = 19982: f(f(19982)) = f(f(2*97*103)) = f(2+97+103) = f(202) = f(2*101) = 2+101 = 103.
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CROSSREFS
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Cf. A022005, A048133, A084932 (primes reached).
Sequence in context: A063176 A083372 A119101 this_sequence A066758 A018888 A115174
Adjacent sequences: A084928 A084929 A084930 this_sequence A084932 A084933 A084934
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KEYWORD
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easy,nonn
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AUTHOR
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Sven Simon (sven-h.simon(AT)t-online.de), Jun 12 2003
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