id:A100020 - OEIS Search Results

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a(n) = smallest prime p such that x^2-n has roots in the p-adic integers.

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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; listen)

	OFFSET	`1,1`
	EXAMPLE	`a(6)=5 because x^2-6 has roots in the 5-adic integers. Roots are` `4+5+45^2+25^4+35^5+25^6+5^7+35^8+O(5^9) and` `1+35+45^3+25^4+5^5+25^6+35^7+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: A151346 A110739 A133154 this_sequence A020638 A091385 A053247` `Adjacent sequences: A100017 A100018 A100019 this_sequence A100021 A100022 A100023`
	KEYWORD	`nonn`
	AUTHOR	`Volker Schmitt (clamsi(AT)gmx.net), Nov 19 2004`

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Last modified December 20 13:54 EST 2009. Contains 171081 sequences.

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