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 A224218 Indices of XOR-positive triangular numbers. That is, numbers n such that triangular(n) XOR triangular(n+1) is a triangular number, where XOR is the bitwise logical XOR operator. 5
 0, 12, 18, 24, 40, 86, 102, 177, 333, 357, 628, 665, 669, 689, 840, 845, 860, 861, 1124, 1185, 1196, 1206, 1377, 1418, 1706, 1890, 1906, 1956, 2138, 2204, 2388, 2524, 2588, 2843, 2970, 2994, 3035, 3107, 3154, 3234, 3299, 3606, 3824, 3854, 4005, 4021, 4169, 4185, 4568, 4580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Generated triangular numbers: A220689(n) = A000217(a(n)) XOR A000217(a(n)+1). Indices of triangular numbers in A220689: A220698. Terms of A220698 that appear in this sequence: A220752. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE Triangular(18) XOR triangular(19) = 171 XOR 190 = 21, because 21 is a triangular number, 18 is in the sequence. MAPLE read("transforms") ; isA000217 := proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then return true else return false; end if; end proc: isA224218 := proc(n) XORnos(A000217(n), A000217(n+1)) ; isA000217(%) ; end proc: A224218 := proc(n) option remember; if n = 1 then 0; else for a from procname(n-1)+1 do if isA224218(a) then return a; end if; end do: end if; end proc: # R. J. Mathar, Apr 23 2013 MATHEMATICA Join[{0}, Flatten[Position[Partition[Accumulate[Range[5000]], 2, 1], _?(OddQ[ Sqrt[1+8BitXor[#[[1]], #[[2]]]]]&), {1}, Heads->False]]] (* Harvey P. Dale, Dec 05 2014 *) 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(i), end=', ') CROSSREFS Cf. A000217, A220689, A220698, A220752, A221643, A220518. Sequence in context: A284342 A198470 A245379 * A076485 A325387 A272860 Adjacent sequences: A224215 A224216 A224217 * A224219 A224220 A224221 KEYWORD nonn,base AUTHOR Alex Ratushnyak, Apr 01 2013 STATUS approved

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Last modified January 27 12:24 EST 2023. Contains 359840 sequences. (Running on oeis4.)