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URL: https://oeis.org/A321291

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A321291
Smallest positive number for which the 4th power cannot be written as sum of 4th powers of any subset of previous terms.
5
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 32, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 56, 64, 68, 72, 76, 80, 84, 88, 92, 96, 104, 108, 112, 128, 136, 144, 152, 160, 168, 176, 184, 192, 208, 216, 224, 256
OFFSET
1,2
COMMENTS
a(n)^4 forms a sum-free sequence.
It is noteworthy that the terms of this sequence increase slower than those of similar sequences for smaller (A321266, A321290) but also larger powers (A321292, A321293).
LINKS
FORMULA
a(n) = 2 * a(n-12) for n > 25 (conjectured).
EXAMPLE
The smallest number > 0 that is not in the sequence is 15, because
15^4 = 4^4 + 6^4 + 8^4 + 9^4 + 14^4.
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 A321291(n):
POWER=4 ; 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), A321292 (5), A321293 (6).
Sequence in context: A322911 A023756 A080944 * A317294 A095736 A380573
KEYWORD
nonn
AUTHOR
Bert Dobbelaere, Nov 02 2018
STATUS
approved