id:A073310 - OEIS Search Results

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a(n) is the smallest number k such that 2+k and 2n+k are both prime.

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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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