A020549 - OEIS

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A020549

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

2, 2, 5, 37, 577, 14401, 518401, 25401601, 1625702401, 131681894401, 13168189440001, 1593350922240001, 229442532802560001, 38775788043632640001, 7600054456551997440001, 1710012252724199424000001, 437763136697395052544000001 (list; graph; refs; listen; history; text; internal format)

	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`

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Last modified August 29 13:25 EDT 2024. Contains 375517 sequences. (Running on oeis4.)