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A020549 revision #42

A020549
a(n) = (n!)^2 + 1.
12
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.
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
KEYWORD
nonn
STATUS
editing