This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
576 is in the list because none of its proper subsequences 5, 7, 6, 57, 76 or 56 are squares.
fQ[n_] := Module[{d = IntegerDigits[n], ds, sq}, ds = FromDigits /@ Union[Most[Rest[Subsets[d]]]]; sq = Select[ds, # > 0 && IntegerQ[Sqrt[#]] &, 1]; sq == {}]; Select[Range[0, 100000]^2, fQ] (* T. D. Noe, Mar 05 2014 *)
isok(n) = {my(d = digits(n)); for (k = 1, #d, for (j= 1, #d - k + 1, if (j != #d, sd = vector(j, i, d[k+i-1]); nsd = fromdigits(sd); if (nsd && issquare(nsd), return(0));););); return (1);} \\ Michel Marcus, Apr 21 2018
# see linked program for faster version
from math import isqrt
from itertools import chain, combinations as C, count, islice
def issquare(n): return isqrt(n)**2 == n
def psets(s): # nonempty proper subsets of s
return chain.from_iterable(C(s, r) for r in range(1, len(s)))
def cond(s):
ss = ("".join(t) for t in psets(s) if t[0] != "0")
return not any(issquare(int(u)) for u in ss)
def agen(): yield from (k**2 for k in count(1) if cond(str(k**2)))
print(list(islice(agen(), 15))) # Michael S. Branicky, Feb 23 2023
1^2 + 2^2 = 5, 3^2 + 4^2 = 25, 6^2 + 7^2 = 85.
filter:= proc(m) local n,i,j,S;
n:= m^2 + (m+1)^2;
S:= {seq(seq(floor((n mod 10^i)/10^j),j=0..i-1),i=1 .. ilog10(n)+1)} minus {n};
not ormap(issqr,S);
end proc:
select(filter, [$0..20000]); # Robert Israel, Dec 09 2024
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