A333436 Partition numbers A000041(k*x_n + y_n) are known to be divisible by prime(n); sequence gives the list of x_n.

5, 7, 11, 17303, 206839, 1977147619

Offset

3,1

Comments

Grime notes that Ramanujan's pattern for a(3), a(4), a(5) or prime(3), prime(4), prime(5) cannot be directly extended to prime(6) = 13, and shows solutions for 13, 17, 19.

Links

Table of n, a(n) for n=3..8.

James Grime and Brady Haran, Partitions, Numberphile video (2016).

Lasse Winquist, An elementary proof of p(11m+6) == 0 (mod 11), J. Combinatorial Theory 6 1969 56--59. MR0236136 (38 #4434).

Example

All {partition( 5k+4)} are divisible by prime(3) = 5, so a(3) = 5.
All {partition( 7k+5)} are divisible by prime(4) = 7, so a(4) = 7.
All {partition(11k+6)} are divisible by prime(5) = 11, so a(5) = 11.

Crossrefs

Cf. A333435 (x_n), A000040 (primes), A000041 (partitions).

Cf. A071734 (p(5k+4)/5), A071746 (p(7k+5)/7), A076394 (p(11k+6)/11).

Cf. A213260 (p(5k+4)).

Sequence in context: A263880 A082565 A309695 * A086255 A306513 A286901

Adjacent sequences: A333433 A333434 A333435 * A333437 A333438 A333439

Keyword

nonn,more

Author

Frank Ellermann, Mar 21 2020

Status

approved