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A341650
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a(n) is the first prime p such that each of the first n primes divides at least one of the composites between p and the next prime.
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2
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2, 3, 5, 7, 13, 19, 61, 113, 113, 113, 113, 113, 773, 773, 773, 887, 887, 2477, 2477, 2477, 2477, 2477, 30727, 31397, 31397, 31397, 31397, 31397, 31397, 155921, 155921, 155921, 221327, 221327, 265621, 265621, 544279, 544279, 1242643, 1242643, 1242643, 1444309, 1444309, 1444309, 1561919, 1561919
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OFFSET
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0,1
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LINKS
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EXAMPLE
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a(6) = 61 because each of the first 6 primes 2,3,5,7,11,13 divides at least one of the composites 62 to 66: 2|62, 3|63, 5|65, 7|63, 11|66 and 13|65.
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MAPLE
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N:= 50: # for a(0) to a(N)
P:= [seq(ithprime(i), i=1..N)]:
V:= Array(0..N): V[0]:= 2: q:= 3: m:= 0:
while m < N do
p:= q; q:= nextprime(p);
E:= mul(i, i=p+1..q-1);
for r from 1 to N do if E mod P[r] <> 0 then break fi od;
r:= r-1;
if r > m then
for s from m+1 to r do V[s]:= p od;
m:= r;
fi;
od:
convert(V, list);
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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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