A096102 - OEIS

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A096102

a(1) = 1, a(2) = 3; for n > 2: a(n) = smallest (odd) number not occurring earlier such that the sum of each section of odd length >=3 is prime.

1, 3, 7, 9, 21, 13 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`If 1, 3, 7, 13 are taken (rather arbitrarily) as starting terms, then the continuation is 17, 31, 11, 25, 5, 37, 341, 163, 647, 571, 989, 3451, 17669, 206413, 6767, 252289, but no number < 10000000 is suited to continue this sequence further.` `There are no further terms. For k to qualify as next term the sums 21+13+k, 7+9+21+13+k and 1+3+7+9+21+13+k have to be prime. One of these sums however is divisible by 3, since 34+k = k+1 (mod 3), 50+k = k+2 (mod 3) and 54+k = k (mod 3). - Klaus Brockhaus, Jul 02 2004`
	EXAMPLE	`1+3+7 = 11, 3+7+9 = 19, 7+9+21 = 37, 9+21+13 = 43, 1+3+7+9+21 = 41, 3+7+9+21+13 = 53 are all prime.`
	CROSSREFS	`Cf. A096100, A096101.` `Sequence in context: A073573 A059621 A034926 * A045797 A118555 A056652` `Adjacent sequences: A096099 A096100 A096101 * A096103 A096104 A096105`
	KEYWORD	`nonn`
	AUTHOR	`Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 24 2004`
	EXTENSIONS	`Edited and corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 29 2004`

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Last modified February 15 03:33 EST 2012. Contains 205694 sequences.