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 A099408 a(n) is the smallest prime p such that x^2+n has roots in the p-adic integers. 1
 5, 3, 7, 5, 3, 5, 2, 3, 5, 7, 3, 7, 7, 3, 2, 5, 3, 3, 5, 3, 5, 13, 2, 5, 5, 3, 7, 2, 3, 11, 2, 3, 7, 5, 3, 5, 19, 3, 2, 7, 3, 13, 11, 3, 3, 5, 2, 7, 5, 3, 5, 7, 3, 5, 2, 3, 11, 31, 3, 2, 5, 3, 2, 5, 3, 5, 17, 3, 5, 17, 2, 3, 7, 3, 7, 5, 3, 19, 2, 3, 5, 7, 3, 5, 11, 3, 2, 13, 3, 7, 5, 2, 17, 5, 2, 5, 7, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE a(7)=2 because x^2+7 has roots in the 2-adic integers. Roots are 1 + 2^2 + 2^4 + 2^5 + 2^7 + O(2^9) and 1 + 2 + 2^3 + 2^6 + 2^8 + O(2^9). MAPLE p:=1; anz:=0; while anz=0 do p:=nextprime(p); poly:=x^2+i; anz:=nops([rootp(poly, p)]); od; a(n):=p; PROG (PARI) { a(n) = forprime(p=2, 10^5, if(!polisirreducible((x^2+n)*(1+O(p))), return(p)) ) } \\ Max Alekseyev, Sep 12 2009 CROSSREFS Sequence in context: A171530 A266684 A173683 * A110265 A275415 A021190 Adjacent sequences:  A099405 A099406 A099407 * A099409 A099410 A099411 KEYWORD nonn AUTHOR Volker Schmitt (clamsi(AT)gmx.net), Nov 17 2004 EXTENSIONS More terms from Max Alekseyev, Sep 12 2009 STATUS approved

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Last modified June 27 08:41 EDT 2022. Contains 354891 sequences. (Running on oeis4.)