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 A213005 a(0)=1, a(n) = least k > a(n-1) such that k*a(n-1) is a triangular number. 2
 1, 3, 5, 9, 17, 33, 45, 72, 143, 152, 303, 420, 451, 603, 952, 1398, 1572, 2408, 3762, 4233, 5880, 6325, 8469, 13384, 20079, 34189, 62769, 82665, 87448, 161037, 287283, 371337, 515745, 533505, 573815, 734484, 737035, 737149, 767505, 825495, 887865, 1136468, 2272935 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Corresponding triangular numbers t(n)=a(n)*a(n+1): 3, 15, 45, 153, 561, 1485, 3240, 10296, 21736, 46056, 127260, 189420, 271953, 574056, 1330896, 2197656, 3785376, 9058896, 15924546, 24890040, 37191000, ... LINKS MATHEMATICA a[0] = 1; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, If[ IntegerQ[ Sqrt[8k*a[n-1]+1] ], Return[k] ] ]; Table[ Print[a[n]]; a[n], {n, 0, 42}] (* Jean-François Alcover, Sep 14 2012 *) PROG (Python) a = 1 for n in range(55): print(a, end=', ') b = k = 0 while k<=a: tn = b*(b+1)//2 k = 0 if tn%a==0: k = tn // a b += 1 a = k CROSSREFS Cf. A000217, A214961. Cf. A081976 (a(0)=1, a(n) = least k > a(n-1) such that k*a(n-1) is a Fibonacci number). Cf. A006882 (a(0)=a(1)=1, a(n) = least k > a(n-1) such that k*a(n-1) is a factorial). Cf. A079078 (a(0)=1, a(n) = least k > a(n-1) such that k*a(n-1) is a primorial). Sequence in context: A074858 A074860 A297300 * A171856 A205537 A135728 Adjacent sequences: A213002 A213003 A213004 * A213006 A213007 A213008 KEYWORD nonn,easy AUTHOR Alex Ratushnyak, Aug 03 2012 STATUS approved

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Last modified December 3 00:23 EST 2022. Contains 358510 sequences. (Running on oeis4.)