A020549 a(n) = (n!)^2 + 1.

2, 2, 5, 37, 577, 14401, 518401, 25401601, 1625702401, 131681894401, 13168189440001, 1593350922240001, 229442532802560001, 38775788043632640001, 7600054456551997440001, 1710012252724199424000001, 437763136697395052544000001

Offset

0,1

Comments

Used to prove there are infinitely many primes of the form 4k+1 (see A282706). - N. J. A. Sloane, Feb 26 2017

References

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 147.

F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 237-240.

H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.

M. Le, On the Interesting Smarandache Product Sequences, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 133-134.

M. Le, The Primes in Smarandache Power Product Sequences, Smarandache Notions Journal, Vol. 9, No. 1-2, 1998, 96-97.

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

M. Fleuren, Smarandache Square Products.

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.

Apoloniusz Tyszka, On sets X, subset of N, whose finiteness implies that we know an algorithm which for every n, element of N, decides the inequality max (X) < n, (2019).

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.

Eric Weisstein's World of Mathematics, Factorial

Eric Weisstein's World of Mathematics, Smarandache Sequences

Maple

with(combinat):seq(fibonacci(3, n!), n=0..16); # Zerinvary Lajos, Apr 21 2008
[seq(n!^2+1, n=0..20)]; # N. J. A. Sloane, Feb 26 2017

Mathematica

Table[(n!)^2 + 1, {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)

Prog

(PARI) a(n)=n!^2 + 1 \\ Charles R Greathouse IV, Nov 30 2016

Crossrefs

Cf. A001044.

For smallest prime factor see A282706.

Sequence in context: A218122 A282706 A301346 * A196128 A227575 A114715

Adjacent sequences: A020546 A020547 A020548 * A020550 A020551 A020552

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved