

A079152


Primes p such that either p1 or p+1 has at most 3 prime factors, counted with multiplicity; i.e., primes p such that either bigomega(p1) <= 3 or bigomega(p+1) <= 3, where bigomega(n) = A001222(n).


5



2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 157, 163, 167, 173, 179, 181, 191, 193, 211, 223, 227, 229, 239, 241, 257, 263, 269, 277, 281, 283, 293, 311, 313, 317, 331
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OFFSET

1,1


COMMENTS

Up to 83, this is the sequence of prime numbers A000040. 89 is not in the sequence because both 891 = 88 = 2*2*2*11 and 89+1 = 90 = 2*3*3*5 have 4 prime factors.


LINKS

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000


EXAMPLE

97 is in the sequence because 97+1 = 98 = 2*7*7 has 3 prime factors.


MATHEMATICA

Select[Prime /@ Range[70], PrimeOmega[#  1] <= 3  PrimeOmega[# + 1] <= 3 & ] (* JeanFrançois Alcover, Jul 02 2013 *)


PROG

(PARI) s(n) = {sr=0; ct=0; forprime(x=2, n, if(bigomega(x1) < 4  bigomega(x+1) < 4, print1(x, ", "); sr+=1.0/x; ct+=1; ); ); print(); print(ct" "sr); } \\ Lists primes p<=n such that either p1 or p+1 has at most 3 prime factors.
(MAGMA) bg:=func<n&+[p[2]: p in Factorization(n)]>; [2] cat [p: p in PrimesInInterval(3, 340) bg(p1) le 3 or bg(p+1) le 3]; // Marius A. Burtea, Jan 16 2020


CROSSREFS

Union of A079150 and A079151. Cf. A079149, A079153.
Sequence in context: A069684 A061022 A238852 * A124590 A049573 A038616
Adjacent sequences: A079149 A079150 A079151 * A079153 A079154 A079155


KEYWORD

nonn


AUTHOR

Cino Hilliard, Dec 27 2002


STATUS

approved



