A160373 Smallest number m such that exactly n triples (p,q,r) of distinct primes exist with m=p*q+r.

1, 11, 13, 23, 17, 37, 53, 62, 81, 99, 93, 105, 118, 122, 148, 152, 165, 166, 208, 224, 214, 225, 232, 250, 284, 285, 308, 314, 332, 346, 326, 382, 388, 400, 448, 476, 458, 494, 454, 518, 520, 478, 525, 530, 578, 598, 640, 602, 632, 716, 634, 740, 710, 692

Offset: 0

Author

Reinhard Zumkeller, May 11 2009

Keywords

• nonn

Comments

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

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

Note that switching p and q does not make a different triple. - Robert Israel, Mar 09 2018

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 0..6567 (n=0..500 from Reinhard Zumkeller)

Programs

Maple

N:= 10^4: # to get terms before the first term > N
Primes:= select(isprime, [2, seq(i,i=3..N,2)]):
V:= Vector(N):
for r in Primes do
  for j from 1 while Primes[j]^2 <= N do
    p:= Primes[j];
    if p = r then next fi;
    for k from j+1 while p*Primes[k]+r <= N do
      q:= Primes[k];
      if q = r then next fi;
      V[p*q+r]:= V[p*q+r]+1;
    od
  od
od:
mv:= max( V):
F:= Vector(mv):
for i from 1 to N do
  if V[i] > 0 and F[V[i]] = 0 then F[V[i]]:= i fi
od:
F0:= min(select(t -> F[t] = 0, [$1..max(V)])):
1, seq(F[i],i=1..F0-1); # Robert Israel, Mar 09 2018
N:= 10^4: # to get terms before the first term > N
Primes:= select(isprime, [2, seq(i,i=3..N,2)]):
V:= Vector(N):
for r in Primes do
  for j from 1 while Primes[j]^2 <= N do
    p:= Primes[j];
    if p = r then next fi;
    for k from j+1 to nops(Primes) while p*Primes[k]+r <= N do
      q:= Primes[k];
      if q = r then next fi;
      V[p*q+r]:= V[p*q+r]+1;
    od
  od
od:
mv:= max( V):
F:= Vector(mv):
for i from 1 to N do
  if V[i] > 0 and F[V[i]] = 0 then F[V[i]]:= i fi
od:
F0:= min(select(t -> F[t] = 0, [$1..max(V)])):
if F0 = infinity then F0:= mv fi:
1, seq(F[i],i=1..F0-1); # Robert Israel, Mar 09 2018