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A167147 a(n) = Number of subsets with n members of the set {1..n^2} such that the sum of the members is prime. 4
4, 26, 444, 11998, 382716, 15844060, 766387489, 42716991304, 2704983373484, 193042233338665, 15032959574223321, 1289808484211222447, 120472472277271660102, 12036408131864572935262, 1297010265532587186011353, 151499235341042432049982767, 18434494194245279115211501310, 2430305919107872967957571237320, 334200348422242729412526022526012 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
The sequence was conceived by Zak Seidov.
Further terms were calculated by Alois P. Heinz.
LINKS
EXAMPLE
When n=2, a(2) = 4 because there are 4 subsets of the set {1,2,3,4} with prime sums: {1,2}=>3, {1,4}=>5, {2,3}=>5, {3,4}=>7.
When n=3, a(3) = 26 because there are 26 subsets of the set {1,2,3,4,5,6,7,8,9} with prime sums: {1,2,4}=>7, {1,2,8}=>11, {1,3,7}=>11, {1,3,9}=>13, {1,4,6}=>11, {1,4,8}=>13, {1,5,7}=>13, {1,7,9}=>17, {2,3,6}=>11, {2,3,8}=>13, {2,4,5}=>11, {2,4,7}=>13, {2,5,6}=>13, {2,6,9}=>17, {2,7,8}=>17, {2,8,9}=>19, {3,4,6}=>13, {3,5,9}=>17, {3,6,8}=>17, {3,7,9}=>19, {4,5,8}=>17, {4,6,7}=>17, {4,6,9}=>19, {4,7,8}=>19, {5,6,8}=>19, {6,8,9}=>23.
MAPLE
g:= proc(n, i, t) option remember;
if n<0 or t<0 then 0
elif n=0 then `if`(t=0, 1, 0)
elif i<1 or i<t or (i+(1-t)/2)*t<n then 0
else g(n, i-1, t) + g(n-i, i-1, t-1)
fi
end;
a:= proc(n) option remember;
add(`if`(isprime(k), g(k, min(k, n^2), n), 0), k=2..n^2*(n^2+1)/2)
end:
seq(a(n), n=2..13);
# Coded by Alois P. Heinz
MATHEMATICA
g[n_, i_, t_] := g[n, i, t] = Which[n<0 || t<0, 0, n == 0, If[t == 0, 1, 0], i<1 || i<t || (i+(1-t)/2)*t < n, 0, True, g[n, i-1, t] + g[n-i, i-1, t-1]]; a[n_] := a[n] = Sum[If[PrimeQ[k], g[k, Min[k, n^2], n], 0], {k, 2, n^2*(n^2 + 1)/2}]; Table[Print[a[n]]; a[n], {n, 2, 13}] (* Jean-François Alcover, Oct 24 2016, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A317668 A328419 A194926 * A322395 A326264 A132488
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)