login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079149 Primes p such that either p-1 or p+1 has at most 2 prime factors, counted with multiplicity; i.e., primes p such that either bigomega(p-1) <= 2 or bigomega(p+1) <= 2, where bigomega(n) = A001222(n). 7
2, 3, 5, 7, 11, 13, 23, 37, 47, 59, 61, 73, 83, 107, 157, 167, 179, 193, 227, 263, 277, 313, 347, 359, 383, 397, 421, 457, 467, 479, 503, 541, 563, 587, 613, 661, 673, 719, 733, 757, 839, 863, 877, 887, 983, 997, 1019, 1093, 1153, 1187, 1201, 1213, 1237 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There are only 2 primes such that both p-1 and p+1 have at most 2 prime factors - 3 and 5. Proof: If p > 5 then whichever of p-1 and p+1 is divisible by 4 has at least 3 prime factors.
Primes which are not the sum of two consecutive composite numbers. - Juri-Stepan Gerasimov, Nov 15 2009
LINKS
MATHEMATICA
Select[Prime[Range[500]], MemberQ[PrimeOmega[{#-1, #+1}], 2]&] (* Harvey P. Dale, Sep 04 2011 *)
PROG
(PARI) s(n) = {sr=0; ct=0; forprime(x=2, n, if(bigomega(x-1) < 3 || bigomega(x+1) < 3, print1(x" "); sr+=1.0/x; ct+=1; ); ); print(); print(ct" "sr); } \\ Lists primes p<=n such that p+-1 has at most 2 prime factors.
CROSSREFS
Union of A079147 and A079148. Cf. A060254, A079152.
Sequence in context: A178576 A360147 A038970 * A343973 A024694 A024320
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 27 2002
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)