login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A135785 Union of A000040, A001248 and A037074. 0
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, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..62.

V. Shevelev, On divisibility of binomial(n-i-1,i-1) by i, Int. J. of Number Theory, 3, no.1 (2007), 119-139.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A138389, A000040, A001248, A037074.

Sequence in context: A032515 A024926 A051532 * A262249 A248421 A008732

Adjacent sequences:  A135782 A135783 A135784 * A135786 A135787 A135788

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 10 2008, May 16 2008

EXTENSIONS

Missing 47 and more terms from Michel Marcus, Dec 04 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)