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.
6786111717//6786111712 = 8237785936 * 8237785942, where // denotes concatenation.
99000099 * 99000103 = 98010199//98010197, where // denotes concatenation.
from itertools import count, islice from sympy import sqrt_mod def A116275_gen(): # generator of terms for j in count(0): b = 10**j a = b*10+1 for k in sorted(sqrt_mod(2,a,all_roots=True)): if a*(b+3) <= k**2-2 < a*(a+2): yield k-2 A116275_list = list(islice(A116275_gen(),30)) # Chai Wah Wu, Feb 19 2024
q:= proc(d,m) local R,t,a,b,x,q;
t:= 10^d+1;
R:= NULL;
for a in numtheory:-divisors(t) do
b:= t/a;
if igcd(a,b) > 1 then next fi;
for x from chrem([0,-m],[a,b]) by t do
q:= x*(x+m)/t;
if q >= 10^d then break fi;
if q >= 10^(d-1) then R:= R, x fi;
od od;
sort(convert({R},list));
end proc:
seq(op(q(d,3)),d=1..10); # Robert Israel, Apr 08 2025
q:= proc(d,m) local R,t,a,b,x,q;
t:= 10^d+1;
R:= NULL;
for a in numtheory:-divisors(t) do
b:= t/a;
if igcd(a,b) > 1 then next fi;
for x from chrem([0,-m],[a,b]) by t do
q:= x*(x+m)/t;
if q >= 10^d then break fi;
if q >= 10^(d-1) then R:= R, x fi;
od od;
sort(convert({R},list));
end proc:
seq(op(q(d,5)),d=1..10); # Robert Israel, Apr 09 2025
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