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A242033
a(n) = lpf(A245024(n)-1), where lpf = least prime factor (A020639).
9
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
OFFSET
1,1
COMMENTS
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
LINKS
MAPLE
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
MATHEMATICA
lpf[n_]:=lpf[n]=First[First[FactorInteger[n]]]; (* least prime factor *)
A242033=Map[lpf[#-1]&, Select[Range[6, 300, 2], lpf[#-1]<lpf[#-3]&] (*A245024*) ] (* Peter J. C. Moses, Aug 14 2014 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Vladimir Shevelev, Aug 12 2014
EXTENSIONS
More terms from Peter J. C. Moses, Aug 12 2014
STATUS
approved