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 A067138 OR-numbral multiplication table, read by antidiagonals. 12
 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 4, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 8, 7, 8, 5, 0, 0, 6, 10, 12, 12, 10, 6, 0, 0, 7, 12, 15, 16, 15, 12, 7, 0, 0, 8, 14, 14, 20, 20, 14, 14, 8, 0, 0, 9, 16, 15, 24, 21, 24, 15, 16, 9, 0, 0, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 0, 0, 11, 20, 27, 32, 31, 28 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS See A048888 for the definition of OR-numbral arithmetic LINKS FORMULA From Rémy Sigrist, Mar 17 2021: (Start) T(n, 0) = 0. T(n, 1) = n. T(n, 2^k) = n*2^k for any k >= 0. T(n, n) = A067398(n). (End) For all n, k: A048720(n,k) <= A(n,k) <= A004247(n,k). - Antti Karttunen, Mar 17 2021 EXAMPLE The top left 0..16 x 0..16 corner of the array: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 0, 3, 6, 7, 12, 15, 14, 15, 24, 27, 30, 31, 28, 31, 30, 31, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 0, 5, 10, 15, 20, 21, 30, 31, 40, 45, 42, 47, 60, 61, 62, 63, 0, 6, 12, 14, 24, 30, 28, 30, 48, 54, 60, 62, 56, 62, 60, 62, 0, 7, 14, 15, 28, 31, 30, 31, 56, 63, 62, 63, 60, 63, 62, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 0, 9, 18, 27, 36, 45, 54, 63, 72, 73, 90, 91, 108, 109, 126, 127, 0, 10, 20, 30, 40, 42, 60, 62, 80, 90, 84, 94, 120, 122, 124, 126, 0, 11, 22, 31, 44, 47, 62, 63, 88, 91, 94, 95, 124, 127, 126, 127, 0, 12, 24, 28, 48, 60, 56, 60, 96, 108, 120, 124, 112, 124, 120, 124, 0, 13, 26, 31, 52, 61, 62, 63, 104, 109, 122, 127, 124, 125, 126, 127, 0, 14, 28, 30, 56, 62, 60, 62, 112, 126, 124, 126, 120, 126, 124, 126, 0, 15, 30, 31, 60, 63, 62, 63, 120, 127, 126, 127, 124, 127, 126, 127, 0, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, . Multiplying 3 ("11" in binary) with itself in this system means taking bitwise-or of "11" with itself, when shifted one bit-position left: 11 110 ------- OR: 111 = 7 in decimal = A(3,3). . Multiplying 10 (= "1010" in binary) and 11 (= "1011" in binary) in this system means taking bitwise-or of binary number 1011 when shifted once left with the same binary number when shifted three bit-positions left: 10110 1011000 ------- OR: 1011110 = 94 in decimal = A(10,11) = A(11,10). PROG (PARI) t(n, k) = {res = 0; for (i=0, length(binary(n))-1, if (bittest(n, i), res = bitor(res, shift(k, i))); ); return (res); } \\ Michel Marcus, Apr 14 2013 CROSSREFS Cf. A003986, A067139, A048888, A007059, A067398 (main diagonal). Cf. also A004247, A048720 for analogous multiplication tables. Sequence in context: A063711 A057893 A048720 * A059692 A353109 A336225 Adjacent sequences: A067135 A067136 A067137 * A067139 A067140 A067141 KEYWORD nonn,tabl,look AUTHOR Jens Voß, Jan 02 2002 EXTENSIONS Example-section rewritten by Antti Karttunen, Mar 17 2021 STATUS approved

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Last modified February 6 03:21 EST 2023. Contains 360091 sequences. (Running on oeis4.)