A333435 Partition numbers A000041(k*x_n + y_n) are known to be divisible by prime(n); sequence gives the list of y_n.

4, 5, 6, 237, 2623, 815655

Offset: 3

Author

Frank Ellermann, Mar 21 2020

Keywords

• nonn
• more

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.

Examples

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

Links

• 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).

Crossrefs

Cf. A333436 (y_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)).