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Search: id:A073684
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| A073684 |
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Sum of next a(n) successive primes is prime. |
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+0
5
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| 2, 3, 5, 3, 5, 3, 3, 7, 9, 5, 9, 7, 3, 7, 5, 3, 3, 3, 5, 3, 3, 3, 5, 5, 57, 25, 49, 3, 9, 5, 11, 3, 5, 5, 5, 5, 17, 25, 3, 3, 5, 3, 7, 9, 5, 3, 3, 3, 15, 3, 3, 3, 3, 3, 3, 3, 15, 3, 5, 33, 5, 3, 3, 9, 7, 3, 33, 3, 3, 5, 3, 15, 3, 5, 9, 7, 13, 5, 11, 3, 3, 11, 9, 5, 5, 17, 7, 3, 13, 5, 3, 11, 13, 15, 35, 5
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Group the primes such that the sum of each group is a prime. Each group from the second onwards should contain at least 3 primes: (2, 3), (5, 7, 11), (13, 17, 19, 23, 29), (31, 37, 41), (43, 47, 53, 59, 61), ... Sequence gives number of terms in each group.
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EXAMPLE
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a(1)=2 because sum of first two primes 2+3 is prime; a(2)=3 because sum of next three primes 5+7+11 is prime; a(3)=5 because sum of next five primes 13+17+19+23+29 is prime.
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MATHEMATICA
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f[l_List] := Block[{n = Length[Flatten[l]], k = 3, r}, While[r = Table[Prime[i], {i, n + 1, n + k}]; ! PrimeQ[Plus @@r], k += 2]; Append[l, r]]; Length /@ Nest[f, {{2, 3}}, 100] (*Chandler*)
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CROSSREFS
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Cf. A073682(n) is the sum of terms in n-th group, A073683(n) is the first term in n-th group, A077279(n) is the last term in n-th group.
Sequence in context: A100742 A001269 A077276 this_sequence A083776 A122820 A151571
Adjacent sequences: A073681 A073682 A073683 this_sequence A073685 A073686 A073687
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 11 2002
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EXTENSIONS
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More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 10 2003
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 02 2007
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