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A089120 Smallest prime factor of n^2 + 1. 22
2, 5, 2, 17, 2, 37, 2, 5, 2, 101, 2, 5, 2, 197, 2, 257, 2, 5, 2, 401, 2, 5, 2, 577, 2, 677, 2, 5, 2, 17, 2, 5, 2, 13, 2, 1297, 2, 5, 2, 1601, 2, 5, 2, 13, 2, 29, 2, 5, 2, 41, 2, 5, 2, 2917, 2, 3137, 2, 5, 2, 13, 2, 5, 2, 17, 2, 4357, 2, 5, 2, 13, 2, 5, 2, 5477, 2, 53, 2, 5, 2, 37, 2, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This includes A002496, primes that are of the form n^2+1.

REFERENCES

H. Rademacher, Lectures on Elementary Number Theory, pp. 33-38.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

a(2k+1)=2; a(10k +/- 2)=5, else a(26k +/- 8)=13, else a(34k +/- 4)=17, else a(58k +/- 12)=29, else a(74k +/- 6)=37,... - M. F. Hasler, Mar 11 2012

A089120(n) = 2 if n is odd, else A089120(n) = min { A002144(k) | n = +/- A209874(k) (mod 2*A002144(k)) }.

MATHEMATICA

Array[FactorInteger[#^2 + 1][[1, 1]] &, {83}] (* Michael De Vlieger, Sep 08 2015 *)

PROG

(PARI) smallasqp1(m) = { for(a=1, m, y=a^2 + 1; f = factor(y); v = component(f, 1); v1 = v[length(v)]; print1(v[1]", ") ) }

(PARI) A089120(n)=factor(n^2+1)[1, 1]  \\ M. F. Hasler, Mar 11 2012

CROSSREFS

Cf. A002496, A014442, A085722, A144255, A193432.

Sequence in context: A098886 A286785 A257514 * A286452 A298664 A319201

Adjacent sequences:  A089117 A089118 A089119 * A089121 A089122 A089123

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Dec 05 2003

STATUS

approved

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)