A328489 Odd numbers k such that the four consecutive odd numbers starting with k have a total of 5 prime factors counting multiplicity.

3, 5, 7, 11, 13, 17, 37, 67, 107, 307, 877, 1297, 2267, 2657, 3457, 3847, 3917, 4787, 4967, 5737, 11827, 12037, 14627, 16447, 18127, 18517, 19417, 20477, 20747, 20897, 21377, 21557, 22567, 22637, 23057, 23557, 23627, 25577, 29567, 31387, 32057, 33347, 33767, 34757, 35797, 36467, 36787, 37307

Offset

1,1

Comments

Numbers k such that A001222(A190577(k))=5.

There are three cases:

k=3.

k, k+4 and k+6 are primes while k+2 is 3 times a prime.

k, k+2 and k+6 are primes while k+4 is 3 times a prime.

All terms > 13 have final digit 7.

The first n for which a(n+1)-a(n)=10 is 7538. - Robert Israel, Oct 19 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3)=7 is in the sequence because 7*9*11*13 is the product of exactly 5 primes: 3*3*7*11*13.

Maple

A1:= select(t -> isprime((t+2)/3) and isprime(t) and isprime(t+4) and isprime(t+6), {seq(i, i=7..100000, 30)}):
A2:= select(t -> isprime((t+4)/3) and isprime(t) and isprime(t+2) and isprime(t+6), {seq(i, i=17..100000, 30)});
sort(convert({3, 5, 11, 13} union A1 union A2, list));

Crossrefs

Cf. A001222, A190577.

Sequence in context: A153602 A136187 A333207 * A130122 A288893 A046494

Adjacent sequences: A328486 A328487 A328488 * A328490 A328491 A328492

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 16 2019

Status

approved