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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 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 <= 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(q0, 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.)