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

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, 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, 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

Offset: 2

Author

Henry Bottomley, Jul 12 2000

Keywords

• easy
• nonn

Comments

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.

Will the most common subsequence seen be (2,3,2)? - Bill McEachen, Jan 30 2011

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n=2..10000

Crossrefs

Cf. A053001, A056929, A056931.

Programs

Maple

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

Mathematica

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

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

Formula

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

Extensions

More terms from James Sellers, Jul 13 2000