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

0,3

Links

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

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 *)

Prog

(Python)
prpr = prev = 1
for n in range(1, 55):
    print prpr,
    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

Crossrefs

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

Sequence in context: A353240 A282167 A076644 * A189626 A338066 A297292

Adjacent sequences: A214958 A214959 A214960 * A214962 A214963 A214964

Keyword

nonn

Author

Alex Ratushnyak, Aug 03 2012

Status

approved