A213005 a(0)=1, a(n) = least k > a(n-1) such that k*a(n-1) is a triangular number.

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, ...

Links

Table of n, a(n) for n=0..42.

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: A074860 A297300 A364543 * A171856 A205537 A135728

Adjacent sequences: A213002 A213003 A213004 * A213006 A213007 A213008

Keyword

nonn,easy

Author

Alex Ratushnyak, Aug 03 2012

Status

approved