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Search: id:A073310
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A073310 a(n) is the smallest number k such that 2+k and 2n+k are both prime. +0
2
1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 5, 3, 1, 1, 5, 3, 1, 3, 1, 1, 3, 1, 5, 3, 1, 5, 3, 1, 1, 5, 3, 1, 3, 1, 1, 5, 3, 1, 3, 1, 5, 3, 1, 11, 5, 3, 1, 3, 1, 1, 3, 1, 1, 3, 1, 17, 11, 9, 11, 5, 3, 1, 3, 1, 5, 3, 1, 1, 9, 9, 5, 3, 1, 1, 5, 3, 1, 5, 3, 1, 3, 1, 5, 3, 1, 5, 3, 1, 1, 9, 9, 5, 3, 1, 1, 3, 1, 1, 11, 9, 29 (list; graph; listen)
OFFSET

1,4

COMMENT

Conjecture: a(n) < 2n. See A073316 for a generalization for all positive even numbers less than 2n.

EXAMPLE

a(45) = 11 because 11 is the smallest number yielding two primes when added to 2 and 90. This is the first instance where this sequence differs from A060266.

MATHEMATICA

maxN=200; lst={}; For[n=1, n<=maxN, n++, k=1; While[k<2n&&!(PrimeQ[k+2]&&PrimeQ[k+2n]), k=k+2]; AppendTo[lst, k]; If[k>2n, Print["Failure at n = ", n]]]; lst

CROSSREFS

Cf. A060266, A073316.

Sequence in context: A101685 A049653 A060266 this_sequence A046929 A068695 A110787

Adjacent sequences: A073307 A073308 A073309 this_sequence A073311 A073312 A073313

KEYWORD

easy,nonn

AUTHOR

T. D. Noe (noe(AT)sspectra.com), Aug 02 2002

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Last modified July 24 12:00 EDT 2008. Contains 142294 sequences.


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