A321292 Smallest positive number for which the 5th power cannot be written as sum of distinct 5th powers of any subset of previous terms.

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, 37, 43, 44, 55, 57, 64, 77, 82, 90, 97, 112, 116, 119, 154, 156, 178, 202, 227, 269, 309, 335, 371, 397, 442, 516, 604, 643, 722, 774, 815, 1000, 1115, 1308, 1503

Offset

1,2

Comments

a(n)^5 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 12, because
12^5 = 4^5 + 5^5 + 6^5 + 7^5 + 9^5 + 11^5.

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 A321292(n):
....POWER=5 ; 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), A321293 (6).

Sequence in context: A035332 A318536 A048991 * A131881 A364728 A053460

Adjacent sequences: A321289 A321290 A321291 * A321293 A321294 A321295

Keyword

nonn

Author

Bert Dobbelaere, Nov 02 2018

Status

approved