login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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