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Search: id:A128039
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| A128039 |
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Numbers n such that 1 - Sum{k=1..n-1}A001223(k)*(-1)^k = 0. |
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3
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| 3, 6, 10, 13, 18, 26, 29, 218, 220, 223, 491, 535, 538, 622, 628, 3121, 3126, 3148, 3150, 3155, 3159, 4348, 4436, 4440, 4444, 4458, 4476, 4485, 4506, 4556, 4608, 4611, 4761, 5066, 5783, 5788, 12528, 1061290, 2785126, 2785691, 2867466, 2867469, 2872437
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sequence has 294 terms < 10^7. Being prime(n) = 3 + 2*(Sum{k=1..n-1}A000040(k)*(-1)^k)), for n odd and, prime(n) =(3 + 2*(Sum{k=1..n-1}A000040(k)*(-1)^k)))*(-1), for n even
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LINKS
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Eric Weisstein's World of Mathematics, Prime Difference Function
Eric Weisstein's World of Mathematics, Prime Sums
Eric Weisstein's World of Mathematics, Alternating Series
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EXAMPLE
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1 - ( -A001223(1) + A001223(2)) = 1-(-1+2) = 0, hence 3 is a term.
1 - ( -A001223(1) + A001223(2) - A001223(3) + A001223(4) - A001223(5)) = 1-(-1+2-2+4-2) = 0, hence 6 is a term.
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MATHEMATICA
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S=0; a=0; Do[S=S+((Prime[k+1]-Prime[k])*(-1)^k); If[1-S==0, a++; Print[a, " ", k+1]], {k, 1, 10^7, 1}]
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CROSSREFS
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Cf. A127596, A001223 (differences between consecutive primes), A000101 (increasing gaps between primes, upper end), A002386 (increasing gaps between primes, lower end), A066033.
Sequence in context: A001952 A047280 A049880 this_sequence A027428 A136850 A079248
Adjacent sequences: A128036 A128037 A128038 this_sequence A128040 A128041 A128042
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KEYWORD
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nonn
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AUTHOR
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Manuel Valdivia (mvaldivia(AT)ugr.es), May 07 2007
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