A077346 Triangle in which n-th row contains n smallest squares beginning with n.

1, 25, 225, 36, 324, 361, 4, 49, 400, 441, 529, 576, 5041, 5184, 5329, 64, 625, 676, 6084, 6241, 6400, 729, 784, 7056, 7225, 7396, 7569, 7744, 81, 841, 8100, 8281, 8464, 8649, 8836, 80089, 9, 900, 961, 9025, 9216, 9409, 9604, 9801, 90000

Offset

1,2

Comments

A018796 contains initial terms of rows. Subsidiary sequence: There can be a rearrangement of squares in groups so that the n-th group contains n squares beginning with n and not occurring earlier. E.g. the initial term of row 25 would be 256 and not 25.

Links

Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Example

Triangle begins:
    1;
   25, 225;
   36, 324,  361;
    4,  49,  400,  441;
  529, 576, 5041, 5184, 5329;
  ...

Maple

g:= proc(n, d)
    local i, r;
    r:= ilog10(n)+1;
    seq(i^2, i = ceil(sqrt(n*10^(d-r))) .. ceil(sqrt((n+1)*10^(d-r)))-1)
end proc:
f:= proc(n)
   local R, count, v, d;
   count:= 0; R:= NULL;
   for d from 1 + ilog10(n) do
     v:= g(n, d);
     R:= R, v;
     count:= count + nops([v]);
     if count >= n then return R[1..n] fi
   od
end proc:
f(1):= 1:
for i from 1 to 10 do f(i) od; # Robert Israel, Jan 28 2025

Prog

(PARI) row(n) = my(list=List(), k=1); while (#list != n, if (strsplit(Str(k^2), Str(n))[1] == "", listput(list, k^2)); k++); Vec(list); \\ Michel Marcus, Feb 08 2023

Crossrefs

Cf. A018796, A077347, A077348, A077349.

Sequence in context: A297864 A065939 A298131 * A351470 A045785 A030484

Adjacent sequences: A077343 A077344 A077345 * A077347 A077348 A077349

Keyword

base,easy,nonn,tabl

Author

Amarnath Murthy, Nov 05 2002

Extensions

More terms from Michel Marcus, Feb 08 2023

Status

approved