A079151 Primes p such that p-1 has at most 3 prime factors, counted with multiplicity; i.e., primes p such that bigomega(p-1) = A001222(p-1) <= 3.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 43, 47, 53, 59, 67, 71, 79, 83, 103, 107, 131, 139, 149, 167, 173, 179, 191, 223, 227, 239, 263, 269, 283, 293, 311, 317, 347, 359, 367, 383, 389, 419, 431, 439, 443, 467, 479, 499, 503, 509, 557, 563, 587, 599, 607, 619, 643

Offset

1,1

Comments

Can it be proved that this is a subsequence of A301590, except for a(5) = 13? (Checked up to A301591(10^4) = 427421.) - M. F. Hasler, Aug 14 2021

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

149 is in the sequence because 149 - 1 = 2*2*37 has 3 prime factors.

Mathematica

s[n_] := Reap[sr = 0; ct = 0; For[x = 2, x <= n, x = NextPrime[x], If[PrimeOmega[x - 1] < 4, Sow[x]; sr += 1.0/x; ct += 1]]][[2, 1]]; s[700] (* Jean-François Alcover, Jun 08 2013, translated and adapted from Pari *)
Select[Prime[Range[120]], PrimeOmega[#-1]<4&] (* Harvey P. Dale, Oct 02 2017 *)

Prog

(PARI) s(n)=sr=0; ct=0; forprime(x=2, n, if(bigomega(x-1) < 4, print1(x" "); sr+=1.0/x; ct+=1; ); ); print(); print(ct" "sr); \\ Lists primes p<=n such that p-1 has at most 3 prime factors.
(PARI) list(lim)=my(v=List([2, 3]), t); forprime(p=2, (lim-1)\2, if(isprime(t=2*p+1), listput(v, t))); forprime(p=2, (lim-1)\4, forprime(q=2, min(p, (lim-1)\2\p), if(isprime(t=2*p*q+1), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 06 2017

Crossrefs

Cf. A079148, A079150, A079152, A079153.

Sequence in context: A129944 A176162 A152900 * A274335 A049643 A005728

Adjacent sequences: A079148 A079149 A079150 * A079152 A079153 A079154

Keyword

easy,nonn

Author

Cino Hilliard, Dec 27 2002

Extensions

Typos in definition corrected by Harvey P. Dale, Oct 02 2017

Status

approved