A255164 - OEIS

A255164

Numbers m such that, starting with prime(m), 10 consecutive primes plus 1 are a product of the same number k of primes (i.e., are k-almost primes).

%I #11 Nov 12 2024 22:17:05

%S 16687573,18163180,19945279,21433861,32241571,41642534,61124701,

%T 84985671,99125673,120180818,132409582,136276974,139516858,149714850,

%U 152735870,160041096,161934847,172578057,177536370,177733590,185207739

%N Numbers m such that, starting with prime(m), 10 consecutive primes plus 1 are a product of the same number k of primes (i.e., are k-almost primes).

%C {A023514(m),..,A023514(m+9)} are of the same value k.

%e a(1)=16687573 because A023514(16687573),..,A023514(16687573+9) are all equal to 4, or

%e prime(16687573,..,16687573+9)=

%e {308495917, 308495947, 308495953, 308496017, 308496043, 308496049, 308496091, 308496157, 308496169, 308496173}, and

%e 308495918=2*23*103*65111, 308495948=2^2*79*976253,

%e 308495954=2*13*127*93427, 308496018=2*3*43*1195721,

%e 308496044=2^2*139*554849, 308496050=2*5^2*6169921,

%e 308496092=2^2*131*588733, 308496158=2*37*317*13151,

%e 308496170=2*5*421*73277, 308496174=2*3*7*7345147.

%Y Cf. A023514, A254787.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 15 2015