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Search: id:A113709
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| A113709 |
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a(n) is the composite between p(n) and p(n+1), where p(n) is the n-th prime, which is divisible by (p(n+1)-p(n)). |
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9
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| 4, 6, 8, 12, 16, 18, 20, 24, 30, 36, 40, 42, 44, 48, 54, 60, 66, 68, 72, 78, 80, 84, 96, 100, 102, 104, 108, 112, 126, 128, 132, 138, 140, 150, 156, 162, 164, 168, 174, 180, 190, 192, 196, 198, 204, 216, 224, 228, 232, 234, 240, 250, 252, 258, 264, 270, 276, 280
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Exactly one composite exists between each p(n+1) and p(n) which is divisible by (p(n+1)-p(n)), for n >= 2.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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a(n)=p(n+1) - (p(n) (mod p(n+1)-p(n))).
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EXAMPLE
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Between the primes 67 and 71 is the composite 68 and 68 is divisible by (71-67)=4. So 68 is in the sequence.
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MATHEMATICA
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f[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, q - Mod[p, q - p]]; Table[ f[n], {n, 2, 60}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A113710, A111379.
Sequence in context: A100390 A157932 A097619 this_sequence A076082 A162648 A062554
Adjacent sequences: A113706 A113707 A113708 this_sequence A113710 A113711 A113712
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Nov 06 2005
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EXTENSIONS
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More terms from Don Reble and Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 07 2005
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