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!)
A303436 Primes p such that all the composite numbers between p and its next prime have no more than 2 distinct prime factors. 0
2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 43, 47, 53, 71, 79, 97, 107, 157, 191, 223, 431, 499, 673, 1151, 1213, 2591, 51199, 139967, 472391, 703123, 786431, 995327, 57395627, 63700991, 169869311, 4076863487, 10871635967 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Supersequence of A078883. Terms that are not there: 2, 7, 13, 19, 23, 31, 37, 43, 47, 53, 79, 97, 157, 223, 499, 673, 1213, 51199, 703123, ...
5*10^11 < a(39) <= 2348273369087. - Giovanni Resta, Apr 26 2018
LINKS
EXAMPLE
157 is in the sequence since it is a prime, and the composite numbers between it and its next prime, 163, have only 2 distinct prime factors: 158 = 2*79, 159 = 3*53, 160 = 2^5*5, 161 = 7*23, and 162 = 2*3^4.
MATHEMATICA
b[n_] := Max[Map[PrimeNu, Range[n + 1, NextPrime[n] - 1]]]; c[n_] := b[Prime[n]]; a={}; Do[If[c[n] < 3, AppendTo[a, Prime[n]]], {n, 1, 10^7}]; a
PROG
(PARI) isok(p) = {if (isprime(p), for(c=p+1, nextprime(p+1)-1, if (omega(c) != 2, return(0)); ); return (1); ); } \\ Michel Marcus, Apr 26 2018
CROSSREFS
Cf. A078883.
Sequence in context: A006514 A216286 A086983 * A334797 A229060 A219528
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Apr 24 2018
EXTENSIONS
a(36) from Michel Marcus, Apr 26 2018
a(37)-a(38) from Giovanni Resta, Apr 26 2018
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 April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)