

A333747


Numbers that are either the product of two consecutive primes or two primes with a prime in between.


3



6, 10, 15, 21, 35, 55, 77, 91, 143, 187, 221, 247, 323, 391, 437, 551, 667, 713, 899, 1073, 1147, 1271, 1517, 1591, 1763, 1927, 2021, 2279, 2491, 2773, 3127, 3233, 3599, 3953, 4087, 4331, 4757, 4891, 5183, 5609, 5767, 6059, 6557, 7031, 7387, 8051, 8633, 8989, 9797, 9991
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OFFSET

1,1


COMMENTS

In other words, these are numbers that are the product of two distinct primes whose prime indices differ by at most two.


LINKS



FORMULA

a(n) = prime(ceiling(n/2))*prime(ceiling((n+3)/2)).
a(2*n1) = prime(n)*prime(n+1).
a(2*n) = prime(n)*prime(n+2).


MAPLE

R:= NULL;
p:= 2; q:= 3;
for n from 1 to 100 by 2 do
r:= nextprime(q);
R:= R, p*q, p*r;
p:= q; q:= r;
od:


MATHEMATICA

a[n_] := Prime[Ceiling[n/2]] * Prime[Ceiling[(n + 3)/2]]; Array[a, 50] (* Amiram Eldar, Apr 04 2020 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



