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A360406
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a(n) = minimal positive k such that prime(n) * prime(n+1) * ... * prime(n+k) - 1 is divisible by prime(n+k+1), or -1 if no such k exists.
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2
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OFFSET
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1,3
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COMMENTS
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Assuming a(9) exists it is greater than 1.75 million.
a(11) = 692, a(12) = 8, a(13) = 792. - Robert Israel, Feb 22 2023
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LINKS
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EXAMPLE
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a(1) = 1 as prime(1) * prime(2) - 1 = 2 * 3 - 1 = 5, which is divisible by prime(3) = 5.
a(2) = 1 as prime(2) * prime(3) - 1 = 3 * 5 - 1 = 14, which is divisible by prime(4) = 7.
a(3) = 9 as prime(3) * ... * prime(12) - 1 = 1236789689134, which is divisible by prime(13) = 41.
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MAPLE
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f:= proc(n) local P, k, p;
P:= ithprime(n); p:= nextprime(P);
for k from 0 to 10^6 do
if P-1 mod p = 0 then return k fi;
p:= nextprime(p);
od;
FAIL
end proc:
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PROG
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(Python)
from sympy import prime, nextprime
p = prime(n)
q = nextprime(p)
s, k = p*q, 1
while (s-1)%(q:=nextprime(q)):
k += 1
s *= q
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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