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.
%I A267509 #43 Jul 07 2021 11:55:26 %S A267509 4,6,8,9,20,22,24,26,28,30,33,36,39,40,42,44,46,48,50,55,60,62,63,64, %T A267509 66,68,69,70,77,80,82,84,86,88,90,93,96,99,100,110,120,121,130,132, %U A267509 140,143,144,150,154,156,160,165,168,169,170,176,180,187,190,198,200 %N A267509 Integers whose base-10 representation (Bm,...,B1,B0) is such that the polynomial f(x) = B0 + B1*x + ... + Bm*x^m is reducible over the ring of integers, 0 <= Bi <= 9. %H A267509 Michel Marcus, <a href="/A267509/b267509.txt">Table of n, a(n) for n = 1..10000</a> %e A267509 4 is a term as f(x) = B0 = 4 = 2*2 = g(x)*h(x) with g(x)=h(x)=2 and neither g(x) nor h(x) is a unit in the integer ring. This implies that f(x) is reducible over the ring of integers. %e A267509 22 is a term as f(x) = B0 + B1*x = 2 + 2*x = 2(1+x) = g(x)*h(x) with g(x)=2 and h(x)=1+x. %e A267509 110 is a term as f(x) = B0 + B1*x + B2*x^2 = 0 + 1*x + 1*x^2 = x + x^2 = x(1+x) = g(x)*h(x) with g(x)=x and h(x)=1+x. %t A267509 okQ[n_] := n<10 && CompositeQ[n] || MatchQ[Factor[(id = IntegerDigits[n]). x^Range[Length[id]-1, 0, -1]][[0]], Times|Power]; Select[Range[250], okQ] (* _Jean-François Alcover_, Feb 01 2016 *) %o A267509 (PARI) isok(n) = {p = Pol(digits(n)); if (poldegree(p) == 0, return ((n!=1) && !isprime(n))); if (! polisirreducible(p), return (1)); f = factor(p); q = prod(k=1, #f~, f[k,1]^f[k,2]); r = p/q; nr = polcoeff(r, 0); if (nr != 1, return (1));} \\ _Michel Marcus_, Jan 31 2016 %o A267509 (PARI) isok(n) = {d = digits(n); p = Pol(d); if (poldegree(p) == 0, return ((n!=1) && !isprime(n))); if (! polisirreducible(p), return (1)); return (gcd(d) != 1);} \\ _Michel Marcus_, Feb 01 2016 %Y A267509 Cf. A121719. %K A267509 nonn,base %O A267509 1,1 %A A267509 _Abdul Gaffar Khan_, Jan 16 2016