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A022897
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Number of solutions to c(1)*prime(2) +...+ c(n)*prime(n+1) = 0, where c(i) = +-1 for i > 1, c(1) = 1.
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5
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0, 0, 0, 0, 0, 1, 0, 2, 0, 7, 0, 19, 0, 63, 0, 197, 0, 645, 0, 2172, 0, 7423, 0, 25534, 0, 89218, 0, 317284, 0, 1130526, 0, 4033648, 0, 14515742, 0, 52625952, 0, 191790090, 0, 702333340, 0, 2585539586, 0, 9570549372, 0, 35562602950, 0, 131774529663, 0
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OFFSET
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1,8
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LINKS
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FORMULA
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a(2n-1) = 0 (odd number of odd terms on the l.h.s.); a(2n) = A083309(n). - M. F. Hasler, Aug 08 2015
a(n) = [x^3] Product_{k=3..n+1} (x^prime(k) + 1/x^prime(k)). - Ilya Gutkovskiy, Jan 26 2024
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EXAMPLE
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a(8) counts these 2 solutions: {3, 5, -7, 11, 13, 17, -19, -23}, {3, 5, 7, 11, -13, -17, -19, 23}. - Clark Kimberling, Oct 01 2013
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MATHEMATICA
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Table[ps = Prime[Range[2, n+1]]; pr = Inner[Times, 2 IntegerDigits[Range[2^(n-1), 2^n - 1], 2, n] - 1, ps, Plus]; Count[pr, 0], {n, 16}] (* T. D. Noe, Sep 30 2013 *)
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PROG
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(PARI) padbin(n, len) = {if (n, b = binary(n), b = [0]); while(length(b) < len, b = concat(0, b); ); b; }
a(n) = {nbs = 0; for (i = 2^(n-1), 2^n-1, vec = padbin(i, n); if (sum(k=1, n, if (vec[k], prime(k+1), -prime(k+1))) == 0, nbs++); ); nbs; } \\ Michel Marcus, Sep 30 2013
(PARI) A022897(n, rhs=0, firstprime=2)={rhs-=prime(firstprime); my(p=vector(n-1, i, prime(i+firstprime))); sum(i=1, 2^#p-1, sum(j=1, #p, (-1)^bittest(i, j-1)*p[j])==rhs)} \\ For illustrative purpose, too slow for n >> 20. - M. F. Hasler, Aug 08 2015
(PARI) a(n, s=0-3, p=2)=if(n<=s, if(s==p, n==s, a(abs(n-p), s-p, precprime(p-1))+a(n+p, s-p, precprime(p-1))), if(s<=0, a(abs(s), sum(i=p+1, p+n-1, prime(i)), prime(p+n-1)))) \\ M. F. Hasler, Aug 09 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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