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A127542
Number of subsets of {1,2,3,...,n} whose sum is prime.
11
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
OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..1000 (first 100 terms from T. D. Noe)
EXAMPLE
The subsets of {1,2,3} that sum to a prime are {1,2}, {2}, {3}, {2,3}. Thus a(3)=4.
MAPLE
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):
seq(a(n), n=1..44); # Alois P. Heinz, Oct 22 2023
MATHEMATICA
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 *)
PROG
(Haskell)
import Data.List (subsequences)
a127542 = length . filter ((== 1) . a010051 . sum) .
subsequences . enumFromTo 1
-- Reinhard Zumkeller, Feb 22 2012, Oct 27 2010
(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
CROSSREFS
Row sums of A282516.
Sequence in context: A268306 A018179 A190165 * A023432 A377252 A072641
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Mar 03 2007
EXTENSIONS
Extended by Ray Chandler, Mar 05 2007
STATUS
approved