A068776 a(0) = 1; for n > 0, a(n) is the smallest triangular number which is a (proper) multiple of a(n-1).

1, 3, 6, 36, 2016, 1493856, 579616128, 11013286048128, 1004811205553955491328, 1897191992473259952000123882626029056, 5012064437680248664058937311304485563631765718940918773832320000

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..13

Example

a(2) = 6, since 6 = 2*a(1) and 6 is a triangular number.

Mathematica

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]=1; a[n_] := a[n]=nexttri[a[n-1]]; (* First do <<NumberTheory`NumberTheoryFunctions`. If lst is a list of relatively prime integers >= 3, pm1[lst] is the list of numbers less than their product and == 1 or -1 (mod every element of lst). nexttri[n] is the smallest triangular number >n and divisible by n. *)

Prog

(PARI) {a068776(m)=local(k, q, n); k=1; q=k*(k+1)/2; while(q<m, n=q; print1(n, ", "); k++; q=q+k; while(q<m&&q%n>0, k++; q=q+k))}
(Python)
from itertools import islice
from sympy import sqrt_mod_iter
def A068776_gen(): # generator of terms
    a = 8
    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
A068776_list = list(islice(A068776_gen(), 12)) # Chai Wah Wu, May 05 2024

Crossrefs

Cf. A000217, A068142.

Sequence in context: A174666 A211893 A093800 * A355544 A359968 A025596

Adjacent sequences: A068773 A068774 A068775 * A068777 A068778 A068779

Keyword

nonn

Author

Klaus Brockhaus, Mar 01 2002

Extensions

Edited by Dean Hickerson, Mar 09 2002

Status

approved