A214961 a(0)=a(1)=1, a(n) = least k > a(n-1) such that k*a(n-2) is a triangular number.

1, 1, 3, 6, 7, 11, 13, 21, 25, 30, 49, 59, 97, 117, 193, 233, 385, 465, 492, 596, 983, 1191, 1965, 2381, 2516, 4761, 5031, 5761, 6290, 8466, 9795, 15470, 15867, 17403, 20559, 24170, 26945, 27192, 27755, 30130, 35235, 43537, 45100, 56805, 58717, 58739, 91000, 117477

Offset: 0

Author

Alex Ratushnyak, Aug 03 2012

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..2100

Crossrefs

Cf. A214914, A214915, A214916, A214963, A213005.

Programs

Maple

f:= proc(a,b)
  local s;
  s:= map(t -> rhs(op(t)), [msolve(x^2=1, 8*a)]);
  min(select(`>`, map(t -> (t^2-1)/(8*a), s), b))
end proc:
A[0]:= 1: A[1]:= 1:
for nn from 2 to 100 do
  A[nn]:= f(A[nn-2],A[nn-1])
od:
seq(A[i],i=0..100); # Robert Israel, Jun 17 2020

Mathematica

a[0]=a[1]=1;a[n_]:=a[n]=(k=a[n-1]+1;While[!IntegerQ@Sqrt[1+8*a[n-2]k],k++];k);Array[a,50,0] (* Giorgos Kalogeropoulos, May 21 2021 *)
lktn[{a_,b_}]:=Module[{k=b+1},While[!OddQ[Sqrt[8a k+1]],k++];{b,k}]; NestList[lktn,{1,1},50][[;;,1]] (* Harvey P. Dale, Sep 09 2023 *)

Python

prpr = prev = 1
for n in range(1, 55):
    print(prpr, end=', ')
    b = k = 0
    while k<=prev:
        d = b*(b+1)//2
        k = 0
        if d%prpr==0:
            k = d // prpr
        b += 1
    prpr = prev
    prev = k