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A306443 Number of ways of partitioning the set of the first n primes into two subsets whose sums differ at most by 1. 5
1, 0, 1, 1, 1, 1, 3, 2, 6, 5, 16, 13, 45, 39, 138, 122, 439, 392, 1417, 1286, 4698, 4341, 16021, 14860, 55146, 51085, 190274, 178402, 671224, 634511, 2404289, 2260918, 8535117, 8067237, 30635869, 29031202, 110496946, 105250449, 401422210, 383579285, 1467402238 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Wikipedia, Partition problem

EXAMPLE

a(8) = 6: 2,17,19/3,5,7,11,13; 3,5,11,19/2,7,13,17; 3,5,13,17/2,7,11,19; 3,7,11,17/2,5,13,19; 2,3,5,11,17/7,13,19; 2,5,7,11,13/3,17,19.

a(9) = 5: 2,3,5,17,23/7,11,13,19; 2,5,7,13,23/3,11,17,19; 2,5,7,17,19/3,11,13,23; 2,5,11,13,19/3,7,17,23; 2,7,11,13,17/3,5,19,23.

MAPLE

s:= proc(n) s(n):= `if`(n=0, 1, ithprime(n)+s(n-1)) end:

b:= proc(n, i) option remember; `if`(i=0, `if`(n<=1, 1, 0),

     `if`(n>s(i), 0, (p->b(n+p, i-1)+b(abs(n-p), i-1))(ithprime(i))))

    end:

a:= n-> ceil(b(0, n)/2):

seq(a(n), n=0..45);

CROSSREFS

Bisections give: A022894 (odd part), A113040 (even part).

Cf. A000040, A069918, A307877.

Sequence in context: A301501 A072787 A293549 * A189073 A107271 A196565

Adjacent sequences:  A306440 A306441 A306442 * A306444 A306445 A306446

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 31 2019

STATUS

approved

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)