A056893 Smallest prime with square excess of n.

2, 3, 7, 13, 41, 31, 23, 89, 73, 59, 47, 61, 113, 239, 79, 97, 593, 139, 163, 461, 277, 191, 167, 193, 281, 251, 223, 317, 353, 991, 431, 761, 433, 563, 359, 397, 521, 479, 439, 569, 617, 571, 619, 773, 829, 887, 947, 673, 1493, 1571, 727, 1013, 953, 1279

Offset: 1

Author

Henry Bottomley, Jul 05 2000

Keywords

• nonn

Examples

			a(4)=13 since 13=3^2+4, while 2, 3, 5, 7 and 11 have square excesses of 1, 2, 1, 3 and 3 respectively.
		

Crossrefs

Cf. A053186, A000196, A002496, A048760, A056892-A056898.

Programs

Maple

A056893 := proc(n)
    local p ;
    p :=2 ;
    while A053186(p) <> n do
        p := nextprime(p) ;
    end do:
    return p ;
end proc: # R. J. Mathar, Jul 28 2013

PARI

A056893(n)={
    local(p=2) ;
    while( A053186(p)!=n,
        p=nextprime(p+1)
    ) ;
    return(p)
} /* R. J. Mathar, Jul 28 2013 */

Formula

a(n) =n+A056894(n).

a(n) = min{p in A000040: A053186(p) = n}. - R. J. Mathar, Jul 28 2013