A308344 -id:A308344 - cp's OEIS frontend

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.

15, 105, 2145, 11628, 94395, 370230, 1565565, 3265290, 13263825, 16689753, 44674878, 62434725, 129757995, 168095280, 190173753, 334822503, 411256860, 659371455, 784892010, 1176876870, 1822721253, 3871076055, 4333386060, 5670113295, 9245348190, 13148662530

Offset: 1

Ali Sada, Jun 01 2021

nonn

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.

This is a subsequence of A011772, which is really the basic sequence here. - N. J. A. Sloane, Jul 06 2021

			15 is the smallest triangular number that is a multiple of 3 and 5, so, a(1) = 15.

Cf. A001359, A006512, A000217, A308344, A002820, A145061.

See also A011772.

a001359(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2};
a(n) = my(p=a001359(n), k = (p-1)*(p+2)/2); k*(k+1)/2; \\ Michel Marcus, Jun 10 2021

For n > 1 a(n) = 3*A001359(n)*A308344(n)*A006512(n-1).

a(n) = A000217(k) = k*(k+1)/2 where k = (A001359(n)-1)*A006512(n)/2. - Jon E. Schoenfield, Jun 01 2021

a(22)-a(26) from Jon E. Schoenfield, Jun 01 2021

cp's OEIS Frontend

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.

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