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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)^6 forms a sum-free sequence.

LINKS

Bert Dobbelaere, Table of n, a(n) for n = 1..150

Wikipedia, Sum-free sequence

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

Adjacent sequences:  A321290 A321291 A321292 * A321294 A321295 A321296

KEYWORD

nonn

AUTHOR

Bert Dobbelaere, Nov 02 2018

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)