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%I #33 Jun 15 2021 18:08:27
%S 1,2,3,4,6,5,7,8,9,20,10,11,12,13,18,14,15,16,17,19,21,22,23,24,31,25,
%T 26,27,28,38,29,30,32,33,45,34,35,36,37,54,39,40,41,42,63,43,44,46,47,
%U 76,48,49,50,51,58,52,53,55,56,73,57,59,60,61,87,62,64,65,66,67,68,69,70,71,83
%N Rearrangement of positive integers such that each five terms sum up to a perfect square.
%C From _Daniel Forgues_, Jan 13 2020: (Start)
%C This sequence is the concatenated rows of a 5 column array of positive integers T(n, k) such that, for row n >= 1:
%C * For 1 <= k <= 4: T(n, k) are the smallest positive integers, in increasing order, not appearing in previous rows;
%C * T(n, 5) is the smallest integer greater than T(n, 4) not appearing in previous rows such that the row sum is a perfect square.
%C The perfect squares seem to be weakly increasing - but are they? (End)
%C No, the sequence of squares is not weakly increasing. For 310 terms, the resulting square is 1600, but for 315 terms it is 1521. - _Michel Marcus_, Jan 17 2020
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a130/A130111.java">Java program</a> (github)
%e 1+2+3+4+6=16, 5+7+8+9+20=49, 10+11+12+13+18=64, 14+15+16+17+19=81.
%e From _Daniel Forgues_, Jan 11 2020: (Start) The array begins:
%e 1, 2, 3, 4, 6: 4^2
%e 5, 7, 8, 9, 20: 7^2
%e 10, 11, 12, 13, 18: 8^2
%e 14, 15, 16, 17, 19: 9^2
%e 21, 22, 23, 24, 31: 11^2
%e 25, 26, 27, 28, 38: 12^2
%e 29, 30, 32, 33, 45: 13^2
%e 34, 35, 36, 37, 54: 14^2
%e 39, 40, 41, 42, 63: 15^2
%e 43, 44, 46, 47, 76: 16^2
%e 48, 49, 50, 51, 58: 16^2
%e 52, 53, 55, 56, 73: 17^2
%e 57, 59, 60, 61, 87: 18^2
%e 62, 64, 65, 66, 67: 18^2
%e ...
%e (End).
%t s={};ra=Range[1000]; Do[su=ra[[1]]+ra[[2]]+ra[[3]]+ra[[4]]; c=5; While[ !IntegerQ[Sqrt[su+ra[[c]]]],c++ ]; rac=ra[[c]]; s=Join[s,{ra[[1]],ra[[2]],ra[[3]],ra[[4]],rac}]; ra=Complement[ra,{ra[[1]],ra[[2]],ra[[3]],ra[[4]],rac}],{50}]; s
%Y Cf. A130108, A130109, A130110.
%K nonn,tabf
%O 1,2
%A _Zak Seidov_, May 08 2007
%E a(73)-a(75) from _Michel Marcus_, Jan 17 2020
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