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%I A344886 #44 Jul 06 2021 02:58:52
%S A344886 15,105,2145,11628,94395,370230,1565565,3265290,13263825,16689753,
%T A344886 44674878,62434725,129757995,168095280,190173753,334822503,411256860,
%U A344886 659371455,784892010,1176876870,1822721253,3871076055,4333386060,5670113295,9245348190,13148662530
%N A344886 a(n) is the smallest triangular number that is a multiple of the product of the members of the n-th pair of twin primes.
%C A344886 If we divide each a(n) by the two primes we get a sequence of the triangular numbers of (3 * A002820(n) - 1). If we take the differences between those triangular numbers we get A145061 + 1.
%C A344886 This is a subsequence of A011772, which is really the basic sequence here. - _N. J. A. Sloane_, Jul 06 2021
%F A344886 For n > 1 a(n) = 3*A001359(n)*A308344(n)*A006512(n-1).
%F A344886 a(n) = A000217(k) = k*(k+1)/2 where k = (A001359(n)-1)*A006512(n)/2. - _Jon E. Schoenfield_, Jun 01 2021
%e A344886 15 is the smallest triangular number that is a multiple of 3 and 5, so, a(1) = 15.
%o A344886 (PARI) a001359(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2};
%o A344886 a(n) = my(p=a001359(n), k = (p-1)*(p+2)/2); k*(k+1)/2; \\ _Michel Marcus_, Jun 10 2021
%Y A344886 Cf. A001359, A006512, A000217, A308344, A002820, A145061.
%Y A344886 See also A011772.
%K A344886 nonn
%O A344886 1,1
%A A344886 _Ali Sada_, Jun 01 2021
%E A344886 a(22)-a(26) from _Jon E. Schoenfield_, Jun 01 2021

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