A068513 a(0) = 15; for n > 0, a(n) is the smallest triangular number which is a (proper) multiple of a(n-1).

15, 45, 630, 25200, 32004000, 508031496000, 128015872500032496000, 3670698694547655407496988066168944000, 10302657959650317880463349610273001290502485245258650172717840000

Offset

0,1

Comments

Thanks to Dean Hickerson for a very efficient program.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10

Mathematica

Needs[ NumberTheory`NumberTheoryFunctions`]; pm1[{k_}] := {1, k - 1}; pm1[lst_] := Module[{a, m, v}, a = lst[[1]]; m = Times @@ Rest[lst]; v = pm1[ Rest[lst]]; Union[ ChineseRemainder[{1, #}, {a, m}] & /@ v, ChineseRemainder[{-1, #}, {a, m}] & /@ v]]; nexttri[1] = 3; nexttri[n_] := Module[{s}, s = (pm1[Power @@ # & /@ FactorInteger[4n]]^2 - 1)/8; For[i = 1, True, i++, If[s[[i]] > n, Return[ s[[i]]] ]]]; a[0] = 15; a[n_] := a[n] = nexttri[ a[n - 1]]; Table[ a[n], {n, 0, 8}]

Prog

(Python)
from itertools import islice
from sympy import sqrt_mod_iter
def A068513_gen(): # generator of terms
    a = 120
    while True:
        yield a>>3
        b = a+1
        for d in sqrt_mod_iter(1, a):
            if d==1 or d**2-1 == a:
                d += a
            if d&1 and d < b:
                b = d
        a = b**2-1
A068513_list = list(islice(A068513_gen(), 10)) # Chai Wah Wu, May 05 2024

Crossrefs

Cf. A068776, A068142.

Sequence in context: A241731 A095129 A219813 * A267079 A290583 A033480

Adjacent sequences: A068510 A068511 A068512 * A068514 A068515 A068516

Keyword

nonn

Author

Robert G. Wilson v, Mar 19 2002

Status

approved