OFFSET
0,1
COMMENTS
By construction, for n >= 2, a(n) == 1 (mod 4) and a(n) > n.
From Robert Israel, Mar 08 2017: (Start)
a(n) <= 2*n+1 if n is in A104636.
The first member of A104636 for which a(n) < 2*n+1 is 48.
a(a(n)-n-1) = a(n). (End)
REFERENCES
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 147.
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 0..74
Apoloniusz Tyszka, On ZFC-formulae phi(x) for which we know a non-negative integer n such that max({x, element of N, phi(x)}) <= n if the set {x, element of N, phi(x)} is finite, 2019.
Apoloniusz Tyszka, Sławomir Kurpaska, Open problems that concern computable sets X, subset of N, and cannot be formally stated as they refer to current knowledge about X, (2020).
Andrew Walker, Table of factors of (n!)^2+1.
MAPLE
f:= proc(n) local a;
a:= min(map(proc(t) if t[1]::integer then t[1] fi end proc, ifactors((n!)^2+1, easy)[2]));
if a = infinity then
a:= traperror(timelimit(60, min(map(t -> t[1], ifactors((n!)^2+1)[2]))));
fi;
a
end proc:
map(f, [$0..36]); # Robert Israel, Mar 08 2017
MATHEMATICA
Join[{2}, Array[FactorInteger[(#!)^2 + 1][[1, 1]]&, {25}]] (* Vincenzo Librandi, Feb 28 2017 *)
PROG
(Magma) [2] cat [Min(PrimeFactors(Factorial(n)^2 + 1)):n in[1..25]]; // Vincenzo Librandi, Feb 28 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 26 2017
EXTENSIONS
More terms from Vincenzo Librandi, Feb 28 2017
STATUS
approved