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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. 6
 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); MATHEMATICA s[n_] := s[n] = If[n == 0, 1, Prime[n] + s[n - 1]]; b[n_, i_] := b[n, i] = If[i==0, If[n <= 1, 1, 0], If[n > s[i], 0, Function[ p, b[n + p, i - 1] + b[Abs[n - p], i - 1]][Prime[i]]]]; a[n_] := Ceiling[b[0, n]/2]; a /@ Range[0, 45] (* Jean-François Alcover, Apr 30 2020, after Alois P. Heinz *) CROSSREFS Bisections give: A022894 (odd part), A113040 (even part). Cf. A000040, A069918, A307877. Sequence in context: A072787 A338524 A293549 * A336518 A189073 A107271 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 January 15 21:50 EST 2021. Contains 340195 sequences. (Running on oeis4.)