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%I #12 Feb 21 2020 13:24:17
%S 0,0,0,1,0,0,2,3,1,0,2,0,1,0,7,6,7,6,8,8,7,6,7,6,6,5,4,4,6,5,6,6,5,4,
%T 3,2,4,3,2,1,2,2,4,3,2,1,2,2,1,0,0,0,1,0,38,38,39,39,40,41,42,42,42,
%U 42,43,43,44,44,44,44,45,46,47,47,48,49,49,49,51,52,52,52,54,54,54,54,54
%N Remainder when n-th composite number is divided by the number of nonprimes not exceeding n.
%H Harry J. Smith, <a href="/A065862/b065862.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = c(n) mod (n - pi(n)) = A002808(n) mod (n - A000720(n)) = A002808(n) mod A062298(n).
%t Module[{nn=150,cmps,len},cmps=Select[Range[nn],CompositeQ];len=Length[ cmps];Mod[#[[1]],#[[2]]-PrimePi[#[[2]]]]&/@Thread[{cmps,Range[len]}]] (* _Harvey P. Dale_, Feb 21 2020 *)
%o (PARI) Composite(n) = { local(k); k=n + primepi(n) + 1; while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); return(k) } { for (n = 1, 1000, a=Composite(n)%(n - primepi(n)); write("b065862.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 02 2009
%Y Cf. A002808, A000720, A062298, A065858-A065864, A065134.
%K nonn
%O 1,7
%A _Labos Elemer_, Nov 26 2001
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