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A321290 Smallest positive number for which the 3rd power cannot be written as sum of 3rd powers of any subset of previous terms. 5
1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 17, 21, 22, 28, 29, 33, 38, 41, 48, 68, 70, 96, 124, 130, 158, 179, 239, 309, 310, 351, 468, 509, 640, 843, 900, 1251, 1576, 1640, 2305, 2444, 2989, 3410, 4575, 5758, 5998, 7490, 8602, 11657, 13017, 15553, 19150, 24411, 25365 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)^3 forms a sum-free sequence.

LINKS

Bert Dobbelaere, Table of n, a(n) for n = 1..100

Wikipedia, Sum-free sequence

EXAMPLE

a(10) = 13. 3rd powers of 14, 15 and 16 can be written as sums of 3rd powers of a subset of the terms {a(1)..a(10)}:

14^3 = 2^3 + 3^3 + 8^3 + 13^3,

15^3 = 4^3 + 5^3 + 7^3 + 8^3 + 10^3 + 11^3,

16^3 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 7^3 + 11^3 + 13^3,

17^3 cannot be written in this way, so a(11) = 17 is the next term.

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 A321290(n):

....POWER=3 ; 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), A321291 (4), A321292 (5), A321293 (6)

Sequence in context: A277992 A180968 A191847 * A274337 A107912 A190850

Adjacent sequences:  A321287 A321288 A321289 * A321291 A321292 A321293

KEYWORD

nonn

AUTHOR

Bert Dobbelaere, Nov 02 2018

STATUS

approved

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Last modified June 12 19:17 EDT 2021. Contains 344959 sequences. (Running on oeis4.)