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A127542
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Number of subsets of {1,2,3,...,n} whose sum is prime.
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11
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0, 2, 4, 7, 12, 22, 42, 76, 139, 267, 516, 999, 1951, 3824, 7486, 14681, 28797, 56191, 108921, 210746, 410016, 804971, 1591352, 3153835, 6249154, 12380967, 24553237, 48731373, 96622022, 191012244, 376293782, 739671592, 1454332766, 2867413428, 5678310305
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The subsets of {1,2,3} that sum to a prime are {1,2}, {2}, {3}, {2,3}. Thus a(3)=4.
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MAPLE
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with(combinat): a:=proc(n) local ct, pn, j:ct:=0: pn:=powerset(n): for j from 1 to 2^n do if isprime(add(pn[j][i], i=1..nops(pn[j]))) =true then ct:=ct+1 else ct:=ct fi: od: end: seq(a(n), n=1..18);
# second Maple program:
b:= proc(n, s) option remember; `if`(n=0,
`if`(isprime(s), 1, 0), b(n-1, s)+b(n-1, s+n))
end:
a:= n-> b(n, 0):
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MATHEMATICA
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g[n_] := Block[{p = Product[1 + z^i, {i, n}]}, Sum[Boole[PrimeQ[k]]*Coefficient[p, z, k], {k, 0, n*(n + 1)/2}]]; Array[g, 34] (* Ray Chandler, Mar 05 2007 *)
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PROG
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(Haskell)
import Data.List (subsequences)
a127542 = length . filter ((== 1) . a010051 . sum) .
subsequences . enumFromTo 1
(PARI) a(n)=my(v=Vec(prod(i=1, n, x^i+1)), s); forprime(p=2, #v, s+=v[p]); s \\ Charles R Greathouse IV, Dec 19 2014
(PARI) first(n)=my(v=vector(n), P=1, s); for(k=1, n, P*=1+'x^n; s=0; forprime(p=2, k*(k+1)/2, s+=polcoeff(P, p)); v[k]=s); v \\ Charles R Greathouse IV, Dec 19 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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