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!)
A135785 Union of A000040, A001248 and A037074. 0

%I #10 Dec 04 2018 07:41:09

%S 2,3,4,5,7,9,11,13,15,17,19,23,25,29,31,35,37,41,43,47,49,53,59,61,67,

%T 71,73,79,83,89,97,101,103,107,109,113,121,127,131,137,139,143,149,

%U 151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241

%N Union of A000040, A001248 and A037074.

%C a(n) possesses the following property: every i not exceeding a(n)/2 for which (a(n),i)>1 does not divide binomial(a(n)-i-1,i-1). Numbers with this property are called "binomial primes". There exist only nine binomial primes which are not terms of this sequence:1,6,8,10,12,20,21,24,33.

%H V. Shevelev, <a href="http://dx.doi.org/10.1142/S179304210700078X">On divisibility of binomial(n-i-1,i-1) by i</a>, Int. J. of Number Theory, 3, no.1 (2007), 119-139.

%t aQ[n_] := PrimeQ[n] || (PrimeNu[n]<3 && Module[{p = FactorInteger[n][[1,1]]}, n==p^2 || (n==p(p+2) && PrimeQ[p+2])]); Select[Range[2, 250], aQ] (* _Amiram Eldar_, Dec 04 2018 *)

%o (PARI) isok(n) = isprime(n) || (issquare(n) && isprime(sqrtint(n))) || (issquare(n+1) && isprime(sqrtint(n+1)-1) && isprime(sqrtint(n+1)+1)); \\ _Michel Marcus_, Dec 04 2018

%Y Cf. A138389, A000040, A001248, A037074.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, May 10 2008, May 16 2008

%E Missing 47 and more terms from _Michel Marcus_, Dec 04 2018

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 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)