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A014442
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Largest prime factor of n^2 + 1.
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13
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2, 5, 5, 17, 13, 37, 5, 13, 41, 101, 61, 29, 17, 197, 113, 257, 29, 13, 181, 401, 17, 97, 53, 577, 313, 677, 73, 157, 421, 53, 37, 41, 109, 89, 613, 1297, 137, 17, 761, 1601, 29, 353, 37, 149, 1013, 73, 17, 461, 1201, 61, 1301, 541, 281, 2917, 89, 3137, 13, 673
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OFFSET
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1,1
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COMMENTS
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All a(n) except a(1) = 2 are the Pythagorean primes, or primes of form 4n+1. Conjecture: every Pythagorean prime appears in a(n) at least once.
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REFERENCES
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H. Rademacher, Lectures on Elementary Number Theory, pp. 33-38.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..5000
J. M. Deshouillers, H. Iwaniec, On the greatest prime factor of n^2+1 Annales de l'institut Fourier, 32 no. 4 (1982), p. 1-11.
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MATHEMATICA
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Table[FactorInteger[n^2+1, FactorComplete->True][[ -1, 1]], {n, 5!}] ..and/or.. Table[Last[Table[ #[[1]]]&/@FactorInteger[n^2+1]], {n, 5!}] ..and/or.. PrimeFactors[n_]:=Flatten[Table[ #[[1]], {1}]&/@FactorInteger[n]]; Table[PrimeFactors[n^2+1][[ -1]], {n, 5!}] [From Vladimir Joseph Stephan Orlovsky, Aug 12 2009]
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PROG
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(PARI) largeasqp1(m) = { for(a=1, m, y=a^2 + 1; f = factor(y); v = component(f, 1); v1 = v[length(v)]; print1(v1", ") ) } (Cino Hilliard)
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CROSSREFS
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Includes primes from A002496.
Cf. A002144 = Pythagorean primes: primes of form 4n+1.
Sequence in context: A089793 A076570 A089121 * A081235 A219586 A082534
Adjacent sequences: A014439 A014440 A014441 * A014443 A014444 A014445
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KEYWORD
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nonn,easy
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AUTHOR
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Glen Burch (gburch(AT)erols.com)
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001
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STATUS
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approved
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