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 A261061 Number of solutions to c(1)*prime(1)+...+c(2n)*prime(2n) = -1, where c(i) = +-1 for i > 1, c(1) = 1. 19
 1, 0, 2, 3, 8, 23, 68, 221, 709, 2344, 8006, 27585, 95114, 335645, 1202053, 4267640, 15317698, 55248527, 200711160, 733697248, 2696576651, 9941588060, 36928160817, 136800727634, 508780005068, 1901946851732, 7133247301621, 26782446410398, 100862459737318 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS There cannot be a solution for an odd number of terms on the l.h.s. because there would be an even number of odd terms but the r.h.s. is odd. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..300 FORMULA Conjecture: limit_{n->infinity} a(n)^(1/n) = 4. - Vaclav Kotesovec, Jun 05 2019 EXAMPLE a(1) = 1 counts the solution prime(1) - prime(2) = -1. a(2) = 0 because prime(1) +- prime(2) +- prime(3) +- prime(4) is always different from -1. a(3) = 2 counts the two solutions prime(1) - prime(2) + prime(3) - prime(4) - prime(5) + prime(6) = -1 and prime(1) - prime(2) - prime(3) + prime(4) + prime(5) - prime(6) = -1. MAPLE s:= proc(n) option remember;       `if`(n<2, 0, ithprime(n)+s(n-1))     end: b:= proc(n, i) option remember; `if`(n>s(i), 0, `if`(i=1, 1,       b(abs(n-ithprime(i)), i-1)+b(n+ithprime(i), i-1)))     end: a:= n-> b(3, 2*n): seq(a(n), n=1..30);  # Alois P. Heinz, Aug 08 2015 MATHEMATICA s[n_] := s[n] = If[n<2, 0, Prime[n]+s[n-1]]; b[n_, i_] := b[n, i] = If[n > s[i], 0, If[i == 1, 1, b[Abs[n-Prime[i]], i-1] + b[n+Prime[i], i-1]]]; a[n_] := b[3, 2*n]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *) PROG (PARI) A261061(n, rhs=-1, firstprime=1)={rhs-=prime(firstprime); my(p=vector(2*n-2+bittest(rhs, 0), 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 >> 10. CROSSREFS Cf. A261062 - A261063 and A261044 (starting with prime(2), prime(3) resp. prime(4)), A022894 - A022904, A083309, A022920 (r.h.s. = 0, 1 or 2), A261057, A261059, A261060, A261045 (r.h.s. = -2). Sequence in context: A241904 A006076 A263459 * A086628 A032096 A301462 Adjacent sequences:  A261058 A261059 A261060 * A261062 A261063 A261064 KEYWORD nonn AUTHOR M. F. Hasler, Aug 08 2015 EXTENSIONS a(14)-a(29) from Alois P. Heinz, Aug 08 2015 STATUS approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)