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%I #8 Nov 21 2016 06:20:58
%S 1,2,3,11,30,9,73,26,56,32,202,55,41,86,45,55,54,58,43,70,107,224,92,
%T 98,110,173,73,115,102,73,140,128,335,97,132,129,109,128,129,113,133,
%U 207,253,301,310,239,180,244,122,152,178,245,249,351,536,262,252,314,202,310
%N a(n) is the smallest number k such that {p(1), p(2), ..., p(k)} contains each residue class mod n, where p(m) is the m-th partition number A000041(m).
%C It has been conjectured that for each r and n, there is some k such that p(k) = r mod n; on that conjecture, this sequence is defined for all n.
%C If congruence classes of p(m) were chosen uniformly at random, the expected value of this sequence would be ~ n log n.
%H Charles R Greathouse IV, <a href="/A278209/b278209.txt">Table of n, a(n) for n = 1..10000</a>
%H Charles R Greathouse IV, <a href="/A278209/a278209.c.txt">C+Arb code for computing this sequence</a>
%e p(1) = 1, p(2) = 2, p(3) = 3, p(4) = 5, p(5) = 7, p(6) = 11, p(7) = 15, p(8) = 22, p(9) = 30, p(10) = 42, and p(11) = 56. Mod 4 these are 1, 2, 3, 1, 3, 3, 3, 2, 2, 2, and 0 respectively. The last term to appear is 0 mod 4 at index 11, so a(4) = 11.
%o (PARI) a(n)=if(n==1, return(1)); my(v=vectorsmall(n),s=1,t,k=1); v[2]=1; while(s<n,t=numbpart(k++)%n; if(v[t+1]==0, v[t+1]=1; if(s++==n, return(k))))
%o (C) See Greathouse link.
%Y Cf. A000041, A278210.
%K nonn
%O 1,2
%A _Charles R Greathouse IV_, Nov 15 2016
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