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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..2100
Programs
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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
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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 *)
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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