

A005529


Primitive prime factors of the sequence k^2 + 1 (A002522) in the order that they are found.
(Formerly M1505)


4



2, 5, 17, 13, 37, 41, 101, 61, 29, 197, 113, 257, 181, 401, 97, 53, 577, 313, 677, 73, 157, 421, 109, 89, 613, 1297, 137, 761, 1601, 353, 149, 1013, 461, 1201, 1301, 541, 281, 2917, 3137, 673, 1741, 277, 1861, 769, 397, 241, 2113, 4357, 449, 2381, 2521, 5477
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OFFSET

1,1


COMMENTS

Primes associated with Stormer numbers.
See A002313 for the sorted list of primes. It can be shown that k^2 + 1 has at most one primitive prime factor; the other prime factors divide m^2 + 1 for some m < k. When k^2 + 1 has a primitive prime factor, k is a Stormer number (A005528), otherwise a nonStormer number (A002312).


REFERENCES

John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 246.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Todd, Table of Arctangents. National Bureau of Standards, Washington, DC, 1951, p. vi.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Stormer Number.
Eric Weisstein's World of Mathematics, Primitive Prime Factor


MATHEMATICA

prms={}; Do[f=First/@FactorInteger[k^2+1]; p=Complement[f, prms]; prms=Join[prms, p], {k, 100}]; prms


PROG

(MAGMA) V:=[]; for n in [1..75] do p:=Max([ x[1]: x in Factorization(n^2+1) ]); if not p in V then Append(~V, p); end if; end for; V; [From Klaus Brockhaus, Oct 29 2008]


CROSSREFS

Cf. A002312, A002313 (primes of the form 4k+1), A002522, A005528.
Sequence in context: A115894 A033835 A178198 * A206029 A057282 A123364
Adjacent sequences: A005526 A005527 A005528 * A005530 A005531 A005532


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Edited by T. D. Noe, Oct 02 2003


STATUS

approved



