This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
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, ...
X[a_, b_] := Module[{A, B, C, x},
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];
T[n_, k_] := Module[{x = BitXor[n-1, 2n-1], k0 = k},
For[i = 1, True, i++, If[n*i == X[x, i],
If[k0 == 1, Return[i], k0--]]]];
Table[T[n-k+1, k], {n, 1, 14}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jan 04 2022 *)
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
read("transforms") ; for n from 0 to 120 do printf("%d,", ORnos(n,4*n) ) ; end do: # R. J. Mathar, Jun 26 2010
f[n_] := BitOr[n, 4n]; Array[f, 58, 0] (* Robert G. Wilson v, Jun 28 2010 *)
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