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 A115872 Square array where row n gives all solutions k > 0 to the cross-domain congruence n*k = A048720(A065621(n),k), zero sequence (A000004) if no such solutions exist. 22
 1, 2, 1, 3, 2, 3, 4, 3, 6, 1, 5, 4, 7, 2, 7, 6, 5, 12, 3, 14, 3, 7, 6, 14, 4, 15, 6, 7, 8, 7, 15, 5, 28, 7, 14, 1, 9, 8, 24, 6, 30, 12, 15, 2, 15, 10, 9, 28, 7, 31, 14, 28, 3, 30, 7, 11, 10, 30, 8, 56, 15, 30, 4, 31, 14, 3, 12, 11, 31, 9, 60, 24, 31, 5, 60, 15, 6, 3, 13, 12, 48, 10, 62, 28, 56, 6, 62, 28, 12, 6, 5, 14, 13, 51, 11, 63, 30, 60, 7, 63, 30, 15, 7, 10, 7 (list; table; 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). Square array is read by descending antidiagonals, as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc. Rows at positions 2^k are 1, 2, 3, ..., (A000027). Row 2n is equal to row n. Numbers on each row give a subset of positions of zeros at the corresponding row of A284270. - Antti Karttunen, May 08 2019 LINKS EXAMPLE Fifteen initial terms of rows 1 - 19 are listed below:    1:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...    2:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...    3:  3,  6,  7,  12,  14,  15,  24,  28,  30,  31,  48,  51,  56,  60,  62, ...    4:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...    5:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...    6:  3,  6,  7,  12,  14,  15,  24,  28,  30,  31,  48,  51,  56,  60,  62, ...    7:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...    8:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...    9: 15, 30, 31,  60,  62,  63, 120, 124, 126, 127, 240, 248, 252, 254, 255, ...   10:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...   11:  3,  6, 12,  15,  24,  27,  30,  31,  48,  51,  54,  60,  62,  63,  96, ...   12:  3,  6,  7,  12,  14,  15,  24,  28,  30,  31,  48,  51,  56,  60,  62, ...   13:  5, 10, 15,  20,  21,  30,  31,  40,  42,  45,  47,  60,  61,  62,  63, ...   14:  7, 14, 15,  28,  30,  31,  56,  60,  62,  63, 112, 120, 124, 126, 127, ...   15: 15, 30, 31,  60,  62,  63, 120, 124, 126, 127, 240, 248, 252, 254, 255, ...   16:  1,  2,  3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,  14,  15, ...   17: 31, 62, 63, 124, 126, 127, 248, 252, 254, 255, 496, 504, 508, 510, 511, ...   18: 15, 30, 31,  60,  62,  63, 120, 124, 126, 127, 240, 248, 252, 254, 255, ...   19:  7, 14, 28,  31,  56,  62,  63, 112, 119, 124, 126, 127, 224, 238, 248, ... PROG (PARI) up_to = 120; A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2); A065621(n) = bitxor(n-1, n+n-1); A115872sq(n, k) = { my(x = A065621(n)); for(i=1, oo, if((n*i)==A048720(x, i), if(1==k, return(i), k--))); }; A115872list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A115872sq(col, (a-(col-1))))); (v); }; v115872 = A115872list(up_to); A115872(n) = v115872[n]; \\ (Slow) - Antti Karttunen, May 08 2019 CROSSREFS Transpose: A114388. First column: A115873. Cf. A048720, A065621, A115857, A115871, A325565, A325566, A325567, A325568, A325570, A325571. Cf. also arrays A277320, A277810, A277820, A284270. A few odd-positioned rows: row 1: A000027, Row 3: A048717, Row 5: A115770 (? Checked for all values less than 2^20), Row 7: A115770, Row 9: A115801, Row 11: A115803, Row 13: A115772, Row 15: A115801 (? Checked for all values less than 2^20), Row 17: A115809, Row 19: A115874, Row 49: A114384, Row 57: A114386. Sequence in context: A201592 A234361 A240450 * A133926 A144337 A143929 Adjacent sequences:  A115869 A115870 A115871 * A115873 A115874 A115875 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Feb 07 2006 EXTENSIONS Example section added and the data section extended up to n=105 by Antti Karttunen, May 08 2019 STATUS approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)