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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

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: 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.)