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A139171
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a(n) = smallest prime number p such that p!/n is an integer.
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3
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2, 2, 3, 5, 5, 3, 7, 5, 7, 5, 11, 5, 13, 7, 5, 7, 17, 7, 19, 5, 7, 11, 23, 5, 11, 13, 11, 7, 29, 5, 31, 11, 11, 17, 7, 7, 37, 19, 13, 5, 41, 7, 43, 11, 7, 23, 47, 7, 17, 11, 17, 13, 53, 11, 11, 7, 19, 29, 59, 5, 61, 31, 7, 11, 13, 11, 67, 17, 23, 7, 71, 7, 73, 37, 11, 19, 11, 13, 79, 7, 11
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OFFSET
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1,1
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LINKS
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MAPLE
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f:= proc(n) local F, m, Q, E, p;
F:= ifactors(n)[2];
m:= nops(F);
Q:= map(t -> t[1], F);
E:= map(t -> t[2], F);
p:= max(Q)-1;
do
p:= nextprime(p);
if andmap(i -> add(floor(p/Q[i]^j), j=1..floor(log[Q[i]](p))) >= E[i], [$1..m]) then return p fi;
od
end proc:
f(1):= 2:
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MATHEMATICA
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a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, Prime[m]], {n, 1, 100}]; a
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PROG
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(PARI) a(n) = forprime(p=2, , if (!(p! % n), return (p))); \\ Michel Marcus, Mar 08 2018
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CROSSREFS
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Prime equivalent of Kempner numbers A002034.
For indices of primes in this sequence see A139169.
Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139166, A139089, A139168-A139170.
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KEYWORD
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AUTHOR
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STATUS
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approved
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