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%I #3 May 04 2024 11:46:37
%S 2,7,11,2,11,5,3,7,2,3,5,11,3,5,7,2,2,7,3,11,5,3,7,5,2,5,11,3,5,7,3,7,
%T 2,3,13,2,3,11,5,3,2,11,3,5,11,3,11,11,2,7,5,3,7,5,3,5,2,3,5,7,3,13,3,
%U 2,2,5,3,2,5,3,5,7,2,5,11
%N a(n) = smallest prime p such that x^2-n has roots in the p-adic integers.
%e a(6)=5 because x^2-6 has roots in the 5-adic integers. Roots are
%e 4+5+4*5^2+2*5^4+3*5^5+2*5^6+5^7+3*5^8+O(5^9) and
%e 1+3*5+4*5^3+2*5^4+5^5+2*5^6+3*5^7+5^8+O(5^9); but this is irreducible over Qp for p in {2,3} (x^2-6 is Eisenstein for p=2 and 3).
%p A100020 := proc(n)
%p local p,anz ;
%p p := 1 ;
%p anz := 0 ;
%p while anz =0 do
%p p := nextprime(p) ;
%p poly := x^2-n ;
%p anz := nops([padic[rootp](poly, p)]);
%p end do:
%p p ;
%p end proc:
%p seq(A100020(n),n=1..100) ;
%Y Cf. A099408.
%K nonn
%O 1,1
%A Volker Schmitt (clamsi(AT)gmx.net), Nov 19 2004
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