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A051342
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Smallest prime factor of 1 + (product of first n primes).
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9
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3, 7, 31, 211, 2311, 59, 19, 347, 317, 331, 200560490131, 181, 61, 167, 953, 73, 277, 223, 54730729297, 1063, 2521, 22093, 265739, 131, 2336993, 960703, 2297, 149, 334507, 5122427, 1543, 1951, 881, 678279959005528882498681487, 87549524399, 23269086799180847
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OFFSET
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1,1
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COMMENTS
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Based on Euclid's proof that there are infinitely many primes.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..87
M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
R. G. Wilson v, Explicit factorizations
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FORMULA
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a(n) = A020639(1+A002110(n)).
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MAPLE
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a:= proc(n)
local N, F, i;
N:= 1 + mul(ithprime(i), i=1..n);
F:= select(type, map(t->t[1], ifactors(N, easy)[2]), integer);
if nops(F) >= 1 then return min(F) fi;
min(map(t->t[1], ifactors(N)[2]))
end proc:
seq(a(n), n=1..40); # Robert Israel, Oct 19 2014
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MATHEMATICA
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Map[FactorInteger,
Table[Product[Prime[n], {n, 1, m}] + 1, {m, 1, 36}]][[All,
1]][[All, 1]] (* Geoffrey Critzer, Oct 19 2014 *)
FactorInteger[#][[1, 1]]&/@(FoldList[Times, Prime[Range[40]]]+1) (* Harvey P. Dale, Oct 08 2021 *)
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PROG
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(PARI) a(n) = factor(1 + prod(i=1, n, prime(i)))[1, 1]; \\ Michel Marcus, Dec 10 2013
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CROSSREFS
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Cf. A014545, A002585.
Sequence in context: A059296 A123332 A343087 * A002585 A103785 A289127
Adjacent sequences: A051339 A051340 A051341 * A051343 A051344 A051345
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer
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EXTENSIONS
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One more term from Michel Marcus, Dec 10 2013
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STATUS
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approved
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