A115874 - OEIS

A115874

Integers i such that 19*i = 55 X i.

0, 7, 14, 28, 31, 56, 62, 63, 112, 119, 124, 126, 127, 224, 238, 248, 252, 254, 255, 448, 455, 476, 496, 504, 508, 510, 511, 896, 910, 952, 992, 1008, 1016, 1020, 1022, 1023, 1792, 1799, 1820, 1823, 1904, 1911, 1984, 1991, 2016, 2032, 2040, 2044

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OFFSET

1,2

COMMENTS

Here * stands for ordinary multiplication and X means carryless (GF(2)[X]) multiplication (A048720).

From Robert Israel, Apr 08 2018: (Start)

n is in the sequence if and only if 2*n is.

If n is in the sequence, then so is (2^k+1)*n if 2^k > n.

Contains 2^k-1 for k >= 5. (End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for sequences defined by congruent products between domains N and GF(2)[X]

MAPLE

X:= proc(a, b) local A, B, C;

A:= convert(a, base, 2);

B:= convert(b, base, 2);

C:= expand(add(A[i]*x^(i-1), i=1..nops(A))*add(B[i]*x^(i-1), i=1..nops(B))) mod 2;

eval(C, x=2)

end proc:

select(t -> 19*t = X(55, t), [$0..10^4]); # Robert Israel, Apr 08 2018

MATHEMATICA

X[a_, b_] := Module[{A, B, C},

A = Reverse@IntegerDigits[a, 2];

B = Reverse@IntegerDigits[b, 2];

C = Expand[

Sum[A[[i]]*x^(i-1), {i, 1, Length[A]}]*

Sum[B[[i]]*x^(i-1), {i, 1, Length[B]}]];

PolynomialMod[C, 2] /. x -> 2];

Select[Range[0, 10^4], 19*# == 55~X~#&] (* Jean-François Alcover, Jan 04 2022, after Robert Israel *)

CROSSREFS

Row 19 of A115872. Superset of A115876? A115875 shows this sequence in binary.

Sequence in context: A232790 A095894 A104599 * A083495 A185066 A089644

Adjacent sequences: A115871 A115872 A115873 * A115875 A115876 A115877

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 07 2006

EXTENSIONS

Offset corrected by Robert Israel, Apr 08 2018

STATUS

approved