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A100020 a(n) = smallest prime p such that x^2-n has roots in the p-adic integers. 0
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, 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, 2, 2, 5, 3, 2, 5, 3, 5, 7, 2, 5, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..75.

EXAMPLE

a(6)=5 because x^2-6 has roots in the 5-adic integers. Roots are

4+5+4*5^2+2*5^4+3*5^5+2*5^6+5^7+3*5^8+O(5^9) and

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).

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;

CROSSREFS

Cf. A099408.

Sequence in context: A110739 A179117 A133154 * A241807 A020638 A091385

Adjacent sequences:  A100017 A100018 A100019 * A100021 A100022 A100023

KEYWORD

nonn

AUTHOR

Volker Schmitt (clamsi(AT)gmx.net), Nov 19 2004

STATUS

approved

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Last modified October 18 14:11 EDT 2021. Contains 348068 sequences. (Running on oeis4.)