[seqfan] Re: A083207 On an observation of Frank Buss.
Donald Alan Morrison
donmorrison at gmail.com
Tue Aug 3 03:16:23 CEST 2010
SeqFans,
I ported a c version of subset sum to sage/python and converted it to
a zumkeller verification function. I verified its correctness for the
first 1137 terms ( 1 < n < 5001 ) in 76.04 seconds. Recall it's the
dynamic programming method where the number of divisors and sigma(n)/2
determines the memory cost (exponentially), and the cpu running time
is supposed to be polynomial, together "pseudo-polynomial". If you
see a bug, please make fun of me promptly!
def is_zk(a):
sa = sigma(a)
if mod(sa,2):
return False
hs = sa/2 # "C" in ssNew.c is sigma(a)/2
d = divisors(a)
n = len(d)
S = (n + 1) * [None]
A = (hs + 1) * [None]
A[0] = 0
S[0] = 0
for i in xrange(1,hs+1):
A[i] = -1
for i in xrange(1,n+1):
S[i] = d[i-1]
for i in xrange(hs):
if A[i] != -1:
for j in xrange(A[i]+1,n+1):
k = i + S[j]
if k > hs:
continue
if (A[k] == -1) or (A[k]>j):
A[k] = j
if hs < 51:
if any(filter(lambda b:b==-1,A[1:hs+1])):
return False
if A[hs] == -1:
return False
else:
return a
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