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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
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, ...
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. 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: A374518 A297300 A364543 * A171856 A205537 A135728
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Aug 03 2012
STATUS
approved