1,1

Primes associated with Stormer numbers.

SeeA002313for 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 non-Stormer number (A002312).

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.

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

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

(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; -Klaus Brockhaus,Oct 29 2008

(PARI) do(n)=my(v=List(), g=1, m, t, f); for(k=1, n, m=k^2+1; t=gcd(m, g); while(t>1, m/=t; t=gcd(m, t)); f=factor(m)[, 1]; if(#f, listput(v, f[1]); g*=f[1])); Vec(v) \\Charles R Greathouse IV,Jun 11 2017

Cf.A002312,A002313(primes of the form 4k+1),A002522,A005528.

Sequence in context:A033835A366609A178198*A259255A274903A206029

Adjacent sequences:A005526A005527A005528*A005530A005531A005532

N. J. A. Sloane.

Edited byT. D. Noe,Oct 02 2003

approved