A160373 - OEIS

%I #8 Mar 09 2018 02:48:22

%S 1,11,13,23,17,37,53,62,81,99,93,105,118,122,148,152,165,166,208,224,

%T 214,225,232,250,284,285,308,314,332,346,326,382,388,400,448,476,458,

%U 494,454,518,520,478,525,530,578,598,640,602,632,716,634,740,710,692

%N Smallest number m such that exactly n triples (p,q,r) of distinct primes exist with m=p*q+r.

%C A100951(a(n)) = n and A100951(m) <> n for m < a(n);

%C a(42) = 525 seems to be the largest odd term.

%C Note that switching p and q does not make a different triple. - _Robert Israel_, Mar 09 2018

%H Robert Israel, <a href="/A160373/b160373.txt">Table of n, a(n) for n = 0..6567</a> (n=0..500 from Reinhard Zumkeller)

%e A100951(37) = #{2*3+31,2*7+23,2*13+11,2*17+3,5*7+2} = 5.

%p N:= 10^4: # to get terms before the first term > N

%p Primes:= select(isprime, [2, seq(i,i=3..N,2)]):

%p V:= Vector(N):

%p for r in Primes do

%p   for j from 1 while Primes[j]^2 <= N do

%p     p:= Primes[j];

%p     if p = r then next fi;

%p     for k from j+1 while p*Primes[k]+r <= N do

%p       q:= Primes[k];

%p       if q = r then next fi;

%p       V[p*q+r]:= V[p*q+r]+1;

%p     od

%p   od

%p od:

%p mv:= max( V):

%p F:= Vector(mv):

%p for i from 1 to N do

%p   if V[i] > 0 and F[V[i]] = 0 then F[V[i]]:= i fi

%p od:

%p F0:= min(select(t -> F[t] = 0, [$1..max(V)])):

%p 1, seq(F[i],i=1..F0-1); # _Robert Israel_, Mar 09 2018

%p N:= 10^4: # to get terms before the first term > N

%p Primes:= select(isprime, [2, seq(i,i=3..N,2)]):

%p V:= Vector(N):

%p for r in Primes do

%p   for j from 1 while Primes[j]^2 <= N do

%p     p:= Primes[j];

%p     if p = r then next fi;

%p     for k from j+1 to nops(Primes) while p*Primes[k]+r <= N do

%p       q:= Primes[k];

%p       if q = r then next fi;

%p       V[p*q+r]:= V[p*q+r]+1;

%p     od

%p   od

%p od:

%p mv:= max( V):

%p F:= Vector(mv):

%p for i from 1 to N do

%p   if V[i] > 0 and F[V[i]] = 0 then F[V[i]]:= i fi

%p od:

%p F0:= min(select(t -> F[t] = 0, [$1..max(V)])):

%p if F0 = infinity then F0:= mv fi:

%p 1, seq(F[i],i=1..F0-1); # _Robert Israel_, Mar 09 2018

%K nonn

%O 0,2

%A _Reinhard Zumkeller_, May 11 2009