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.
1089 = 33^2 is a concatenation of 10 and 89, 10+89 = 99.
f:= proc(k) local F,x,p,t; p:= 10^k-1; F:= select(t -> t[2]::odd, ifactors(p)[2]); x:= mul(t[1],t=F); seq(j^2*x*p, j=ceil(sqrt((10^(k-1)+1)/x))..floor(sqrt(p/x))) end proc: map(f, [$1..20]); # Robert Israel, Sep 09 2020
from itertools import count, islice from math import prod, isqrt from sympy import factorint def A084006_gen(): # generator of terms for l in count(1): m = 10**l-1 x = prod(p for p, e in factorint(m).items() if e&1) yield from (j**2*x*m for j in range(isqrt(10**(l-1)//x)+1,isqrt(m//x)+1)) A084006_list = list(islice(A084006_gen(),20)) # Chai Wah Wu, Mar 20 2025
from itertools import count, islice from math import prod, isqrt from sympy import factorint def A084007_gen(): # generator of terms for l in count(1): m = 10**l-1 x = prod(p for p, e in factorint(m).items() if e&1) y = isqrt(x*m) yield from (j*y for j in range(isqrt(10**(l-1)//x)+1,isqrt(m//x)+1)) A084007_list = list(islice(A084007_gen(),30)) # Chai Wah Wu, Mar 20 2025
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