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A056893 Smallest prime with square excess of n.

%I A056893 #11 Jul 28 2013 17:39:31
%S A056893 2,3,7,13,41,31,23,89,73,59,47,61,113,239,79,97,593,139,163,461,277,
%T A056893 191,167,193,281,251,223,317,353,991,431,761,433,563,359,397,521,479,
%U A056893 439,569,617,571,619,773,829,887,947,673,1493,1571,727,1013,953,1279
%N A056893 Smallest prime with square excess of n.
%F A056893 a(n) =n+A056894(n).
%F A056893 a(n) = min{p in A000040: A053186(p) = n}. - _R. J. Mathar_, Jul 28 2013
%e A056893 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.
%p A056893 A056893 := proc(n)
%p A056893     local p ;
%p A056893     p :=2 ;
%p A056893     while A053186(p) <> n do
%p A056893         p := nextprime(p) ;
%p A056893     end do:
%p A056893     return p ;
%p A056893 end proc: # _R. J. Mathar_, Jul 28 2013
%o A056893 (PARI) A056893(n)={
%o A056893     local(p=2) ;
%o A056893     while( A053186(p)!=n,
%o A056893         p=nextprime(p+1)
%o A056893     ) ;
%o A056893     return(p)
%o A056893 } /* _R. J. Mathar_, Jul 28 2013 */
%Y A056893 Cf. A053186, A000196, A002496, A048760, A056892-A056898.
%K A056893 nonn
%O A056893 1,1
%A A056893 _Henry Bottomley_, Jul 05 2000