This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333435 #32 Apr 09 2020 03:14:17
%S A333435 4,5,6,237,2623,815655
%N A333435 Partition numbers A000041(k*x_n + y_n) are known to be divisible by prime(n); sequence gives the list of y_n.
%C A333435 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.
%H A333435 James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=NjCIq58rZ8I">Partitions</a>, Numberphile video (2016).
%H A333435 Lasse Winquist, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80105-5">An elementary proof of p(11m+6) == 0 (mod 11)</a>, J. Combinatorial Theory 6 1969 56--59. MR0236136 (38 #4434).
%e A333435 All {partition( 5k+4)} are divisible by prime(3) = 5, so a(3) = 4.
%e A333435 All {partition( 7k+5)} are divisible by prime(4) = 7, so a(4) = 5.
%e A333435 All {partition(11k+6)} are divisible by prime(5) = 11, so a(5) = 6.
%Y A333435 Cf. A333436 (y_n), A000040 (primes), A000041 (partitions).
%Y A333435 Cf. A071734 (p(5k+4)/5), A071746 (p(7k+5)/7), A076394 (p(11k+6)/11).
%Y A333435 Cf. A213260 (p(5k+4)).
%K A333435 nonn,more
%O A333435 3,1
%A A333435 _Frank Ellermann_, Mar 21 2020