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Search: id:A082467
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| A082467 |
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Least k such that n-k and n+k are both primes. |
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9
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| 1, 2, 1, 4, 3, 2, 3, 6, 1, 6, 3, 2, 3, 6, 1, 12, 3, 2, 9, 6, 5, 6, 3, 4, 9, 12, 1, 12, 9, 4, 3, 6, 5, 6, 9, 2, 3, 12, 1, 24, 3, 2, 15, 6, 5, 12, 3, 8, 9, 6, 7, 12, 3, 4, 15, 12, 1, 18, 9, 4, 3, 6, 5, 6, 15, 2, 3, 12, 1, 6, 15, 4, 3, 6, 5, 18, 9, 2, 15, 24, 5, 12, 3, 14, 9, 18, 7, 12, 9, 4, 15, 6, 7, 30, 9
(list; graph; listen)
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OFFSET
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4,2
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COMMENT
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The existence of k for all n >= 4 is equivalent to Goldbach's Conjecture that every even number >= 4 is the sum of two primes.
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n = 4..5000
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FORMULA
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A078496(n)-a(n) = A078587(n)+a(n) = n.
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EXAMPLE
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n=10: k=3 because 10-3 and 10+3 are both prime, and 3 is the smallest k such that n +/- k are both prime.
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MATHEMATICA
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f[n_] := Block[{k}, If[OddQ[n], k = 2, k = 1]; While[ !PrimeQ[n - k] || !PrimeQ[n + k], k += 2]; k]; Table[ f[n], {n, 4, 98}] (from Robert G. Wilson v Mar 28 2005)
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PROGRAM
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(PARI) a(n)=if(n<0, 0, k=1; while(isprime(n-k)*isprime(n+k) == 0, k++); k)
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CROSSREFS
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Cf. A087695, A087696, A087697, A087678, A087679, A087680, A087681, A087682, A087683, A087711.
Cf. A129301 (records), A129302 (where records occur).
Sequence in context: A109977 A080079 A087712 this_sequence A106407 A023141 A072650
Adjacent sequences: A082464 A082465 A082466 this_sequence A082468 A082469 A082470
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 27 2003
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EXTENSIONS
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Entries checked by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 08 2007
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