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 A115874 Integers i such that 19*i = 55 X i. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified December 9 17:46 EST 2022. Contains 358703 sequences. (Running on oeis4.)