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

Author

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

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A001222, A190577.

Programs

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));