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A344886 revision #42

A344886

a(n) is the least 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

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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.

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.