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 A022894 Number of solutions to c(1)*prime(1) +...+ c(2n+1)*prime(2n+1) = 0, where c(i) = +-1 for i > 1, c(1) = 1. 30
 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, 51938115653565 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS c(1)*prime(1) +...+ c(2n)*prime(2n) = 0 has no solution, because the l.h.s. has an odd number of odd terms and the r.h.s. is even. LINKS T. D. Noe and Ray Chandler, Table of n, a(n) for n = 0..1000 (first 101 terms from T. D. Noe) FORMULA Conjecture: limit_{n->infinity} a(n)^(1/n) = 4. - Vaclav Kotesovec, Jun 05 2019 EXAMPLE a(1) = 1 because +2 +3 -5 = 0, a(2) = 1 because +2 -3 +5 +7 -11 = 0, a(3) = 2 because +2 +3 -5 -7 +11 +13 -17 = +2 +3 -5 +7 -11 -13 +17 = 0. a(4) = 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. MAPLE sp:= proc(n) sp(n):= `if`(n=1, 0, ithprime(n)+sp(n-1)) end: b := proc(n, i) option remember; `if`(n>sp(i), 0, `if`(i=1, 1,         b(n+ithprime(i), i-1)+ b(abs(n-ithprime(i)), i-1)))      end: a:= n-> b(2, 2*n+1): seq(a(n), n=0..40);  # Alois P. Heinz, Aug 05 2012 MATHEMATICA 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} ] PROG (PARI) A022894={a(n, s=0-prime(1), p=1)=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), max(sum(i=p+1, p+(p>1)+2*n, prime(i)), 1), prime(p+(p>1)+2*n))))} \\ M. F. Hasler, Aug 09 2015 CROSSREFS Cf. A113040, A215036, A083309 (sums of odd primes). Cf. A022895, A022896 (r.h.s. = 1 & 2, using all primes), A083309 and A022897 - A022899 (using primes >= 3), A022900 - A022902 (using primes >=5), A022903, A022904, A022920 (using primes >= 7); A261061 - A261063 & A261045 (r.h.s. = -1); A261057, A261059, A261060 & A261044 (r.h.s. = -2). Bisection (odd part) of A306443. Sequence in context: A319378 A151446 A239106 * A149861 A148305 A104447 Adjacent sequences:  A022891 A022892 A022893 * A022895 A022896 A022897 KEYWORD nonn,nice AUTHOR EXTENSIONS Edited by Robert G. Wilson v, Jan 29 2002 More terms from T. D. Noe, Jan 16 2007 Edited by M. F. Hasler, Aug 09 2015 STATUS approved

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Last modified October 17 22:05 EDT 2019. Contains 328134 sequences. (Running on oeis4.)