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

Author

Ali Sada, Jun 01 2021

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

See also A011772.

Programs

PARI

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

Formula

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

Extensions

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