|
%I #9 Dec 08 2018 17:25:56
%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,25,26,27,28,30,
%T 37,43,44,55,57,64,77,82,90,97,112,116,119,154,156,178,202,227,269,
%U 309,335,371,397,442,516,604,643,722,774,815,1000,1115,1308,1503
%N Smallest positive number for which the 5th power cannot be written as sum of distinct 5th powers of any subset of previous terms.
%C a(n)^5 forms a sum-free sequence.
%H Bert Dobbelaere, <a href="/A321292/b321292.txt">Table of n, a(n) for n = 1..150</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sum-free_sequence">Sum-free sequence</a>
%e The smallest number > 0 that is not in the sequence is 12, because
%e 12^5 = 4^5 + 5^5 + 6^5 + 7^5 + 9^5 + 11^5.
%o (Python)
%o def findSum(nopt, tgt, a, smax, pwr):
%o ....if nopt==0:
%o ........return [] if tgt==0 else None
%o ....if tgt<0 or tgt>smax[nopt-1]:
%o ........return None
%o ....rv=findSum(nopt-1, tgt - a[nopt-1]**pwr, a, smax, pwr)
%o ....if rv!=None:
%o ........rv.append(a[nopt-1])
%o ....else:
%o ........rv=findSum(nopt-1,tgt, a, smax, pwr)
%o ....return rv
%o def A321292(n):
%o ....POWER=5 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
%o ....while len(a)<n:
%o ........while True:
%o ............x+=1
%o ............lst=findSum(len(a), x**POWER, a, smax, POWER)
%o ............if lst==None:
%o ................break
%o ............rhs = " + ".join(["%d^%d"%(i,POWER) for i in lst])
%o ............print(" %d^%d = %s"%(x,POWER,rhs))
%o ........a.append(x) ; sumpwr+=x**POWER
%o ........print("a(%d) = %d"%(len(a),x))
%o ........smax.append(sumpwr)
%o ....return a[-1]
%Y Other powers: A321266 (2), A321290 (3), A321291 (4), A321293 (6).
%K nonn
%O 1,2
%A _Bert Dobbelaere_, Nov 02 2018
|
