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A321293
Smallest positive number for which the 6th power cannot be written as sum of distinct 6th powers of any subset of previous terms.
5
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 42, 43, 51, 57, 60, 61, 71, 74, 88, 91, 99, 112, 116, 117, 132, 152, 153, 176, 203, 228, 244, 256, 281, 293, 345, 392, 439, 441, 529, 594, 627
OFFSET
1,2
COMMENTS
a(n)^6 forms a sum-free sequence.
LINKS
EXAMPLE
The smallest number > 0 that is not in the sequence is 25, because 25^6 = 1^6 + 2^6 + 3^6 + 5^6 + 6^6 + 7^6 + 8^6 + 9^6 + 10^6 + 12^6 + 13^6 + 15^6 + 16^6 + 17^6 + 18^6 + 23^6.
PROG
(Python)
def findSum(nopt, tgt, a, smax, pwr):
if nopt==0:
return [] if tgt==0 else None
if tgt<0 or tgt>smax[nopt-1]:
return None
rv=findSum(nopt-1, tgt - a[nopt-1]**pwr, a, smax, pwr)
if rv!=None:
rv.append(a[nopt-1])
else:
rv=findSum(nopt-1, tgt, a, smax, pwr)
return rv
def A321293(n):
POWER=6 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
while len(a)<n:
while True:
x+=1
lst=findSum(len(a), x**POWER, a, smax, POWER)
if lst==None:
break
rhs = " + ".join(["%d^%d"%(i, POWER) for i in lst])
print(" %d^%d = %s"%(x, POWER, rhs))
a.append(x) ; sumpwr+=x**POWER
print("a(%d) = %d"%(len(a), x))
smax.append(sumpwr)
return a[-1]
CROSSREFS
Other powers: A321266 (2), A321290 (3), A321291 (4), A321292 (5).
Sequence in context: A044921 A260423 A193989 * A246091 A175427 A246098
KEYWORD
nonn
AUTHOR
Bert Dobbelaere, Nov 02 2018
STATUS
approved