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!)
A056927 Difference between n^2 and largest prime less than n^2. 9

%I #36 Aug 02 2020 02:24:10

%S 1,2,3,2,5,2,3,2,3,8,5,2,3,2,5,6,7,2,3,2,5,6,5,6,3,2,11,2,13,8,3,2,3,

%T 2,5,2,5,10,3,12,5,2,3,8,3,2,7,2,23,8,5,6,7,2,15,20,3,12,7,2,11,2,3,6,

%U 7,6,3,2,11,2,5,6,5,2,27,2,5,12,3,8,5,6,13,6,3,8,3,2,7,8,3,2,5,12,7,6,3

%N Difference between n^2 and largest prime less than n^2.

%C Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2 is equivalent to the conjecture that a(n) < 2n-1 for all n>1.

%C Will the most common subsequence seen be (2,3,2)? - _Bill McEachen_, Jan 30 2011

%H T. D. Noe, <a href="/A056927/b056927.txt">Table of n, a(n) for n=2..10000</a>

%F a(n) = A000290(n)-A053001(n).

%e a(4)=3 because largest prime less than 4^2 is 13 and 16-13=3.

%p A056927 := n-> n^2-prevprime(n^2); seq(A056927(n), n=2..100);

%t Table[n2=n^2;n2-NextPrime[n2,-1],{n,2,100}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 09 2011 *)

%o (PARI){my(maxx=10000);n=2;ptr=2;while(n<=maxx,q=n^2;pp=precprime(q); diff=q-pp;print(ptr," ",diff);n++;ptr++ );} \\ _Bill McEachen_, May 07 2014

%Y Cf. A053001, A056929, A056931.

%K easy,nonn

%O 2,2

%A _Henry Bottomley_, Jul 12 2000

%E More terms from _James A. Sellers_, Jul 13 2000

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 08:00 EDT 2024. Contains 371265 sequences. (Running on oeis4.)