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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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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
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EXAMPLE
| 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
| 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);
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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] (*Chandler*)
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PROG
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2010: (Start)
(Other) Haskell:
import Data.List (subsequences)
sieve (p:ns) = p:sieve [n | n <- ns, mod n p > 0]
primes = sieve [2..]
isPrime n = e primes where e (p:ps) = p == n || p < n && e ps
a127542 n = length $ filter (isPrime . sum) $ subsequences [1..n]
-- eop. (End)
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CROSSREFS
| Cf. A053632, A126024.
Cf. A181522. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2010]
Sequence in context: A000072 A018179 A190165 * A023432 A072641 A135360
Adjacent sequences: A127539 A127540 A127541 * A127543 A127544 A127545
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 03 2007
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 05 2007
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