A068858 a(1) = 3 = 1*3; a(n) = smallest multiple of a(n-1) which is a product of two consecutive odd numbers.

3, 15, 195, 4095, 2477475, 448422975, 19384876786275, 70676639845770308825475, 11604095937711402889585984522057770447375, 56023729629975618843823135187551800751351023283966800458449243286895375

Offset: 1

Author

Amarnath Murthy, Mar 12 2002

Keywords

• nonn

Comments

The multiple is assumed to be nontrivial, i.e. a(n) > a(n-1) as otherwise all terms are equal to 3. - Chai Wah Wu, May 05 2024

Examples

			195 = 13*15 belongs to this sequence and the smallest multiple of 195 which is a product of two consecutive odd numbers is 4095 = 63*65.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A068857.

Programs

Maple

f:= proc(x) local V,V1,y;
     V:= map(t -> rhs(op(t))-1, [msolve(r^2=1,x)]);
     V:= map(t -> `if`(t*(t+2)=x, t + x, t), V);
     y:= min(map(t -> `if`(t::even, t+x, t), V));
     y*(y+2)
end proc:
A[1]:= 3:
for n from 2 to 11 do A[n]:= f(A[n-1]) od:
seq(A[i],i=1..11); # Robert Israel, May 14 2017

Python

from itertools import islice
from sympy import sqrt_mod_iter
def A068858_gen(): # generator of terms
    a = 3
    while True:
        yield a
        b = a+1
        for d in sqrt_mod_iter(1,a):
            if d**2-1 == a:
                d += a
            if d&1:
                d += a
            if d < b:
                b = d
        a = b**2-1
A068858_list = list(islice(A068858_gen(),11)) # Chai Wah Wu, May 05 2024

Extensions

More terms from Sascha Kurz, Mar 23 2002

Corrected by Robert Israel, May 14 2017