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Search: id:A022894
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| A022894 |
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Number of solutions to c(1)p(1)+...+c(2n+1)p(2n+1) = 0, where c(i) = +-1 for i>1, c(1) = 1, p(i) = primes. |
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+0
8
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| 0, 1, 1, 2, 5, 13, 39, 122, 392, 1286, 4341, 14860, 51085, 178402, 634511, 2260918, 8067237, 29031202, 105250449, 383579285, 1404666447, 5171065198, 19141008044, 71124987313, 263548339462, 983424096451, 3684422350470, 13818161525284
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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c(1)p(1)+..+c(2n)p(2n) = 0 has no solution.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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EXAMPLE
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a(0) = 1 because +2 +3 -5 = 0, a(1) = 1 because +2 -3 +5 +7 -11 = 0, a(2) = 2 because +2 +3 -5 -7 +11 +13 -17 = +2 +3 -5 +7 -11 -13 +17 = 0.
a(3) = 5 because +2 -3 -5 +7 +11 +13 +17 -19 -23 = +2 -3 +5 -7 +11 +13 -17 +19 -23 = +2 -3 +5 +7 -11 -13 +17 +19 -23 = +2 -3 +5 +7 -11 +13 -17 -19 +23 = +2 +3 +5 -7 -11 -13 +17 -19 +23 = 0 and there are no others up through the ninth prime.
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MATHEMATICA
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Do[a = Table[ Prime[i], {i, 1, n} ]; c = 0; k = 2^(n - 1); While[k < 2^n, If[ Apply[ Plus, a*(-1)^(IntegerDigits[k, 2] + 1)] == 0, c++ ]; k++ ]; Print[c], {n, 1, 32, 2} ]
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CROSSREFS
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Cf. A083309 (sums of odd primes)
Sequence in context: A001475 A000800 A006823 this_sequence A104447 A127986 A133448
Adjacent sequences: A022891 A022892 A022893 this_sequence A022895 A022896 A022897
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KEYWORD
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nonn,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 29 2002
More terms from T. D. Noe (noe(AT)sspectra.com), Jan 16 2007
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