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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A065377.

Sequence in context: A293833 A146316 A258803 * A308143 A308515 A361328

Adjacent sequences: A157492 A157493 A157494 * A157496 A157497 A157498

Keyword

nonn

Author

Cino Hilliard, Mar 01 2009

Extensions

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

Status

approved