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
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
KEYWORD
nonn,tabf
AUTHOR
Zak Seidov, May 08 2007
EXTENSIONS
a(73)-a(75) from Michel Marcus, Jan 17 2020
STATUS
approved