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 A220689 Triangular numbers generated in A224218. That is, the triangular numbers generated by the operation triangular(i) XOR triangular(i+1) along increasing i. 3
 1, 21, 21, 105, 105, 105, 105, 946, 946, 666, 1653, 666, 1378, 946, 1225, 946, 4005, 1378, 4005, 1378, 7381, 1225, 1378, 1653, 2485, 4005, 31125, 4005, 4005, 4005, 2485, 13861, 13861, 5356, 4005, 7381, 5356, 5356, 7381, 4005, 5356, 29161, 12561, 12561, 4186, 4186, 4186, 4186 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..48. FORMULA a(n) = A000217(A224218(n)) XOR A000217(A224218(n)+1). MAPLE read("transforms") ; A220689 := proc(n) i := A224218(n) ; XORnos(A000217(i), A000217(i+1)) ; end proc: # R. J. Mathar, Apr 23 2013 MATHEMATICA nmax = 100; pmax = 2 nmax^2; (* increase coeff 2 if A224218 is too short *) A224218 = Join[{0}, Flatten[Position[Partition[Accumulate[Range[pmax]], 2, 1], _?(OddQ[Sqrt[1 + 8 BitXor[#[[1]], #[[2]]]]]&), {1}, Heads -> False]]]; a[n_] := Module[{i}, i = A224218[[n]]; BitXor[PolygonalNumber[i], PolygonalNumber[i+1]]]; Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Aug 07 2023, after Harvey P. Dale in A224218 *) PROG (Python) def rootTriangular(a): sr = 1<<33 while a < sr*(sr+1)//2: sr>>=1 b = sr>>1 while b: s = sr+b if a >= s*(s+1)//2: sr = s b>>=1 return sr for i in range(1<<12): s = (i*(i+1)//2) ^ ((i+1)*(i+2)//2) t = rootTriangular(s) if s == t*(t+1)//2: print(str(s), end=', ') CROSSREFS Cf. A000217, A224218, A224511. Sequence in context: A371100 A048245 A246034 * A056485 A056475 A219913 Adjacent sequences: A220686 A220687 A220688 * A220690 A220691 A220692 KEYWORD nonn AUTHOR Alex Ratushnyak, Apr 13 2013 STATUS approved

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Last modified June 12 19:52 EDT 2024. Contains 373360 sequences. (Running on oeis4.)