A157495 The smallest prime difference between prime(n) and any smaller square.

2, 2, 5, 3, 2, 13, 13, 3, 7, 13, 31, 37, 5, 7, 11, 17, 23, 61, 3, 7, 37, 43, 2, 53, 61, 37, 3, 7, 73, 13, 127, 31, 37, 103, 5, 7, 13, 19, 23, 29, 79, 37, 47, 157, 53, 3, 67, 79, 2, 193, 37, 43, 97, 107, 61, 7, 13, 127, 241, 137, 139, 37, 163, 167, 277, 61, 7, 13, 23, 313, 29, 103

Offset: 1

Author

Cino Hilliard, Mar 01 2009

Keywords

• nonn
• look

Comments

If the only preceding square k such that p-k^2 is prime is 0, then we generate sequence A065377.

Examples

			The 7th prime is 17. The preceding squares of 17 are 16,9,4,1,0. The differences are 17-16=1, 17-9=8, 17-4=13, 17-1=16 and 17-0=17. Then 4 is the first preceding square of 17 that can be subtracted from 17 to get a prime. So a(7)=13. If we reduce the prime(6)=13 in this fashion, we have 13-9=4, 13-1=12, 13-0=13. This shows that 0 is the first square that can be subtract from 13 to get a prime number. So a(6)=13.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A065377.

Programs

Maple

A157495 := proc(n)
    local p,s ;
    p := ithprime(n) ;
    s := floor(sqrt(p)) ;
    while not isprime(p-s^2) do
        s := s-1;
    end do;
    p-s^2 ;
end proc:
seq(A157495(n),n=1..130) ; # R. J. Mathar, Sep 07 2016

Mathematica

Table[SelectFirst[Reverse[p-Range[0,Floor[Sqrt[p]]]^2],PrimeQ],{p, Prime[ Range[80]]}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 23 2017 *)

PARI

g(n)= c=0; forprime(x=2,n,for(k=1,n^2,if(issquare(abs(x-k)) && isprime(k), print1(k","); c++; break))); c

Extensions

NAME rephrased for clarity. - R. J. Mathar, Sep 08 2016