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

%I A077346 #17 Jan 29 2025 12:23:40
%S A077346 1,25,225,36,324,361,4,49,400,441,529,576,5041,5184,5329,64,625,676,
%T A077346 6084,6241,6400,729,784,7056,7225,7396,7569,7744,81,841,8100,8281,
%U A077346 8464,8649,8836,80089,9,900,961,9025,9216,9409,9604,9801,90000
%N A077346 Triangle in which n-th row contains n smallest squares beginning with n.
%C A077346 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.
%H A077346 Robert Israel, <a href="/A077346/b077346.txt">Table of n, a(n) for n = 1..10011</a> (first 141 rows, flattened)
%e A077346 Triangle begins:
%e A077346     1;
%e A077346    25, 225;
%e A077346    36, 324,  361;
%e A077346     4,  49,  400,  441;
%e A077346   529, 576, 5041, 5184, 5329;
%e A077346   ...
%p A077346 g:= proc(n,d)
%p A077346     local i,r;
%p A077346     r:= ilog10(n)+1;
%p A077346     seq(i^2, i = ceil(sqrt(n*10^(d-r))) .. ceil(sqrt((n+1)*10^(d-r)))-1)
%p A077346 end proc:
%p A077346 f:= proc(n)
%p A077346    local R,count,v,d;
%p A077346    count:= 0; R:= NULL;
%p A077346    for d from 1 + ilog10(n) do
%p A077346      v:= g(n,d);
%p A077346      R:= R,v;
%p A077346      count:= count + nops([v]);
%p A077346      if count >= n then return R[1..n] fi
%p A077346    od
%p A077346 end proc:
%p A077346 f(1):= 1:
%p A077346 for i from 1 to 10 do f(i) od; # _Robert Israel_, Jan 28 2025
%o A077346 (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
%Y A077346 Cf. A018796, A077347, A077348, A077349.
%K A077346 base,easy,nonn,tabl
%O A077346 1,2
%A A077346 _Amarnath Murthy_, Nov 05 2002
%E A077346 More terms from _Michel Marcus_, Feb 08 2023