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A260187
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a(n) = n modulo the greatest primorial <= n.
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2
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0, 0, 1, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0
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OFFSET
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1,8
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COMMENTS
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I think this can help in finding prime numbers.
If n>2 and a(n)=0 then n is not prime.
If n>2 and 2 <= a(n) <= p with p = A006530(A260188(n)) (i.e., greatest prime factor of A260188(n)) then n is not prime.
If n>2 and (a(n) mod k) = 0 and 2 <= k <= p with p = A006530(A260188(n)) (i.e., greatest prime factor of A260188(n)) then n is not prime.
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 1 because 5 modulo 2# = 1 and 2# = 2 is the greatest primorial <= 5. (3# = 2*3 = 6 > 5)
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MAPLE
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N:= 100: # to get a(1) to a(N)
P:= 1: p:= 2: R:= 2:
for n from 1 to N do
if n >= R then
P:= R; p:= nextprime(p); R:= P*p;
fi;
A[n]:= n mod P;
od:
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MATHEMATICA
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s = Product[Prime@ n, {n, #}] & /@ Range[0, 6]; Table[Mod[n, Last@ Select[s, # <= n &]], {n, 120}] (* Michael De Vlieger, Jul 20 2015 *)
f[n_] := Block[{m = p = 1}, While[p*(m + 1) <= n, p = p*m; m = NextPrime@ m]; Mod[n, p]]; Array[f, 101] (* Robert G. Wilson v, Jul 21 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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