A133662
Lexically least increasing sequence such that the sum of any nonempty subsequence is not a square.
Original entry on oeis.org
2, 3, 5, 10, 27, 38, 120, 258, 907, 2030, 3225, 8295, 15850, 80642, 378295, 1049868, 3031570, 12565348, 34530254, 122586800, 415026860, 1454069870, 4870827425, 18129394322, 77805478498
Offset: 1
10 is here because none of 10, 10+2, 10+3, 10+5, 10+2+3, 10+2+5, 10+3+5 and 10+2+3+5 are square numbers.
Definition corrected by
Don Reble, Jan 01 2008
A305884
Lexicographically first sequence of positive squares, no two or more of which sum to a square.
Original entry on oeis.org
1, 1, 1, 4, 16, 25, 25, 324, 841, 1849, 2601, 14884, 18769, 103041, 292681, 774400, 3400336, 13307904, 34892649, 179399236, 582643044, 2008473856, 4369606609, 22833627664, 67113119844, 251608579236, 1240247504896, 3174109249609
Offset: 1
All terms are positive, so a(1) = 1; likewise, a(2) = a(3) = 1.
a(4) cannot be 1, because the first 4 terms would then sum to 4 = 2^2; however, no two or more terms of {1, 1, 1, 4} sum to a square, so a(4) = 4.
a(5) cannot also be 4, because 4 + 4 + 1 = 9 = 3^2, nor can it be 9, since 9 + 4 + 1 + 1 + 1 = 16 = 4^2, but a(5) = 16 satisfies the definition.
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a = {1}; Do[n = Last@a; s = Select[Union[Total /@ Subsets[a^2]], # >= n &];
While[AnyTrue[s, IntegerQ@ Sqrt[n^2 + #] &], n++]; AppendTo[a, n], {14}]; a^2 (* Giovanni Resta, Jun 14 2018 *)
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from sympy import integer_nthroot
from sympy.utilities.iterables import multiset_combinations
A305884_list, n, m = [], 1, 1
while len(A305884_list) < 30:
for l in range(1,len(A305884_list)+1):
for d in multiset_combinations(A305884_list,l):
if integer_nthroot(sum(d)+m,2)[1]:
break
else:
continue
break
else:
A305884_list.append(m)
continue
n += 1
m += 2*n-1 # Chai Wah Wu, Jun 19 2018
Showing 1-2 of 2 results.
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