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A068142 a(0) = 21; for n > 0, a(n) is the smallest triangular number which is a (proper) multiple of a(n-1). 3
21, 105, 210, 630, 25200, 32004000, 508031496000, 128015872500032496000, 3670698694547655407496988066168944000, 10302657959650317880463349610273001290502485245258650172717840000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..9.

EXAMPLE

a(1) = 105, since 105 = 5*21 = 5*a(0), 105 is a triangular number and 2*a(0) = 42, 3*a(0) = 63, 4*a(0) = 84 are not triangular numbers.

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]=21; 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) {a068142(m)=local(k, q, n); k=6; 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))}

CROSSREFS

Cf. A000217, A068776.

Sequence in context: A201468 A306259 A069499 * A126229 A060537 A116689

Adjacent sequences:  A068139 A068140 A068141 * A068143 A068144 A068145

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Feb 22 2002

EXTENSIONS

Edited and extended by Klaus Brockhaus, Robert G. Wilson v, Mar 01 2002 and Dean Hickerson, Mar 09 2002

STATUS

approved

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)