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A242033
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a(n)=lpf(A245024(n)-1), where lpf=least prime factor (A020639).
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9
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3, 3, 3, 5, 3, 3, 3, 3, 7, 3, 5, 3, 3, 3, 3, 3, 5, 3, 7, 3, 3, 3, 3, 5, 3, 3, 3, 7, 3, 3, 5, 3, 3, 3, 3, 13, 3, 5, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 5, 3, 3, 3, 11, 3, 7, 3, 5, 3, 3, 3, 3, 3, 5, 3, 7, 3, 3, 3, 11, 3, 5, 3, 3, 3, 7, 3, 3, 5, 3, 19, 3, 3, 3, 3, 5
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OFFSET
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1,1
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COMMENTS
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Conjecture. The sequence contains all odd primes.
The conjecture is true. Consider n-1 = p*q where p is an odd prime and q is a prime > p such that q == p^(-1) mod r for every odd prime r < p. Such primes q exist by Dirichlet's theorem on primes in arithmetic progressions. - Robert Israel, Aug 13 2014
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LINKS
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MAPLE
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lpf:= n -> min(numtheory:-factorset(n)):
L:= [seq(lpf(2*i+1), i=1..1000)]:
L[select(i->L[i] < L[i-1], [$2..nops(L)])]; # Robert Israel, Aug 13 2014
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MATHEMATICA
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lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]]; (* least prime factor *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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