The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A306043 Lexicographically first sequence of distinct positive squares, no two or more of which sum to a square. 1
 1, 4, 9, 25, 49, 64, 484, 625, 1225, 2209, 12100, 57600, 67600, 287296, 1517824, 7452900, 19492225, 64352484, 161391616, 976375009, 3339684100, 9758278656, 33371982400, 81598207716, 448192758784, 1641916765129, 4148028762241, 23794464493849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If the squares were not required to be distinct, sequence A305884 would result. LINKS EXAMPLE All terms are distinct positive squares, and no two or more of the first three positive squares sum to a square, so a(1) = 1^2 = 1, a(2) = 2^2 = 4, and a(3) = 3^2 = 9. a(4) cannot be 16, because 16 + a(3) = 16 + 9 = 25 = 5^2, but a(4) = 25 satisfies the definition. a(5) cannot be 36, because 36 + 9 + 4 = 49 = 7^2, but a(5) = 49 satisfies the definition. MATHEMATICA a = {1}; Do[n = 1 + Last@a; s = Select[Union[Total /@ Subsets[a^2]], # >= n &]; While[AnyTrue[s, IntegerQ@Sqrt[n^2 + #] &], n++]; AppendTo[a, n], {12}]; a^2 (* Giovanni Resta, Jun 19 2018 *) PROG (Python) from itertools import combinations from sympy import integer_nthroot A306043_list, n, m = [], 1, 1 while len(A306043_list) < 30:     for l in range(1, len(A306043_list)+1):         for d in combinations(A306043_list, l):             if integer_nthroot(sum(d)+m, 2)[1]:                 break         else:             continue         break     else:         A306043_list.append(m)     n += 1     m += 2*n-1 # Chai Wah Wu, Jun 19 2018 CROSSREFS Cf. A305884. Sequence in context: A069557 A230312 A332646 * A194269 A336230 A130283 Adjacent sequences:  A306040 A306041 A306042 * A306044 A306045 A306046 KEYWORD nonn AUTHOR Jon E. Schoenfield, Jun 17 2018 EXTENSIONS a(24)-a(26) from Giovanni Resta, Jun 19 2018 a(27)-a(28) from Jon E. Schoenfield, Jul 21 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 11:44 EDT 2021. Contains 345048 sequences. (Running on oeis4.)