A242033 - OEIS

A242033

a(n) = lpf(A245024(n)-1), where lpf = least prime factor (A020639).

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A020639, A065091, A242034, A243937, A245024.

Sequence in context: A011277 A376659 A084742 * A375848 A301738 A302387