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A356457
a(n) is the least number that can be written in exactly n ways as p*q + q*r + p*r where (p,q,r) is an unordered triple of distinct primes.
1
1, 31, 71, 151, 191, 491, 671, 887, 311, 1151, 1391, 1751, 1031, 2711, 2831, 3911, 1991, 3191, 5351, 9551, 7031, 20951, 8951, 8711, 10631, 5591, 15431, 10391, 15791, 28031, 20471, 17111, 48191, 27191, 31391, 39191, 52631, 35591, 42311, 61871, 50951, 92231, 70391, 108071, 99431, 103991, 96071
OFFSET
0,2
COMMENTS
Empirical observation: It appears that the majority of the members of this sequence end in 1, and nearly all the rest end in 9.
Conjecture: a(n) = A003415(A007304(k)) and a(n) is the least number where at least n solutions for k exist. - Thomas Scheuerle, Aug 08 2022
LINKS
EXAMPLE
a(3) = 151 because 151 is the first number that can be written in exactly 3 ways: 151 = 3*7 + 3*13 + 7*13 = 3*5 + 3*17 + 5*17 = 2*3 + 2*29 + 3*29.
MAPLE
M:= 10^5: # to get terms before the first term > M
V:= Vector(M): p:= 1:
do
p:= nextprime(p);
if 5*p+6 > M then break fi;
q:= 1;
do
q:= nextprime(q);
if q = p or p*q + 2*(p+q) > M then break fi;
r:= 1;
do
r:= nextprime(r);
if r = q then break fi;
v:= p*q + p*r + q*r;
if v > M then break fi;
V[v]:= V[v]+1;
od od od:
m:= max(V):
W:= Array(0..m):
for i from 1 to M do
if W[V[i]] = 0 then W[V[i]]:= i fi
od:
if member(0, W, 'k') then m:= k-1 fi:
convert(W[0..m], list);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Aug 07 2022
STATUS
approved