A321293 Smallest positive number for which the 6th power cannot be written as sum of distinct 6th powers of any subset of previous terms.

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

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