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A130111 Rearrangement of positive integer such that each five terms sum up to a perfect square. 4
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, 26, 27, 28, 38, 29, 30, 32, 33, 45, 34, 35, 36, 37, 54, 39, 40, 41, 42, 63, 43, 44, 46, 47, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Daniel Forgues, Jan 13 2020: (Start)

This sequence is the concatenated rows of a 5 column array of positive integers T(n, k) such that, for row n >= 1:

* For 1 <= k <= 4: T(n, k) are the smallest positive integers, in increasing order, not appearing in previous rows;

* 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.

The perfect squares seem to be weakly increasing - but are they? (End)

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

LINKS

Table of n, a(n) for n=1..75.

Sean A. Irvine, Java program (github)

EXAMPLE

1+2+3+4+6=16, 5+7+8+9+20=49, 10+11+12+13+18=64, 14+15+16+17+19=81.

From Daniel Forgues, Jan 11 2020: (Start) The array begins:

   1,  2,  3,  4,  6:  4^2

   5,  7,  8,  9, 20:  7^2

  10, 11, 12, 13, 18:  8^2

  14, 15, 16, 17, 19:  9^2

  21, 22, 23, 24, 31: 11^2

  25, 26, 27, 28, 38: 12^2

  29, 30, 32, 33, 45: 13^2

  34, 35, 36, 37, 54: 14^2

  39, 40, 41, 42, 63: 15^2

  43, 44, 46, 47, 76: 16^2

  48, 49, 50, 51, 58: 16^2

  52, 53, 55, 56, 73: 17^2

  57, 59, 60, 61, 87: 18^2

  62, 64, 65, 66, 67: 18^2

...

(End).

MATHEMATICA

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

CROSSREFS

Cf. A130108, A130109, A130110.

Sequence in context: A057508 A057164 A085175 * A104182 A332805 A332807

Adjacent sequences:  A130108 A130109 A130110 * A130112 A130113 A130114

KEYWORD

nonn,tabf

AUTHOR

Zak Seidov, May 08 2007

EXTENSIONS

a(73)-a(75) from Michel Marcus, Jan 17 2020

STATUS

approved

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Last modified July 10 03:35 EDT 2020. Contains 335570 sequences. (Running on oeis4.)