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

1,1

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

Links

Table of n, a(n) for n=1..26.

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

Example

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

Prog

(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

Crossrefs

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

See also A011772.

Sequence in context: A226109 A264415 A319588 * A165892 A349169 A077261

Adjacent sequences: A344883 A344884 A344885 * A344887 A344888 A344889

Keyword

nonn

Author

Ali Sada, Jun 01 2021

Extensions

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

Status

approved