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A267509 Integers n having base 10 representation (Bm,...,B1,B0) such that the polynomial f(x) = B0 + B1x + ... + Bmx^m is reducible over ring of integers, 0 <= Bi <= 9. 3
4, 6, 8, 9, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 42, 44, 46, 48, 50, 55, 60, 62, 63, 64, 66, 68, 69, 70, 77, 80, 82, 84, 86, 88, 90, 93, 96, 99, 100, 110, 120, 121, 130, 132, 140, 143, 144, 150, 154, 156, 160, 165, 168, 169, 170, 176, 180, 187, 190, 198, 200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

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) and h(x) is a unit in integer ring. This implies that f(x) is reducible over ring of integers.

22 is a term as f(x)=B0+B1x=2+2x=2(1+x)=g(x)*h(x) with g(x)=2 and h(x)=1+x.

110 is a term as f(x)=B0+B1x+B2x^2=0+1x+1x^2=x+x^2=x(1+x)=g(x)*h(x) with g(x)=x and h(x)=1+x.

MATHEMATICA

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-Fran├žois Alcover, Feb 01 2016 *)

PROG

(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

(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

CROSSREFS

Cf. A121719.

Sequence in context: A075243 A024370 A121719 * A162738 A161600 A032350

Adjacent sequences:  A267506 A267507 A267508 * A267510 A267511 A267512

KEYWORD

nonn,base

AUTHOR

Abdul Gaffar Khan, Jan 16 2016

STATUS

approved

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Last modified April 23 09:35 EDT 2019. Contains 322385 sequences. (Running on oeis4.)