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 A173321 a(n) = 4*n! - 1. 7
 3, 3, 7, 23, 95, 479, 2879, 20159, 161279, 1451519, 14515199, 159667199, 1916006399, 24908083199, 348713164799, 5230697471999, 83691159551999, 1422749712383999, 25609494822911999, 486580401635327999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Bernard Schott, Jul 11 2019: (Start) With this sequence, it is possible to prove that there are infinitely many prime numbers of the form 4*k+3. Prove that: 1. Every prime factor of a(n) is > n, and, 2. All these prime factors are of the form 4*k+1 or 4*k+3. 3. There is at least one prime of the form 4*k+3 > n, 4. The set of prime numbers of the form 4*k+3 is infinite. Indeed, for n >= 1, the successive prime factors of a(n) that are of the form 4*k+3 are 3, 7, 23, 19, 479, 2879, 19, 179, ... (End) REFERENCES Transmath, Term S, SpĂ©cialitĂ©, Programme 2002, Nathan, 2002, Exercice 82 p. 93. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) = n*a(n-1) + n - 1 for n > 0, a(0) = 3. - Vincenzo Librandi, Sep 30 2013 MAPLE A173321:=n->4*n! - 1; seq(A173321(n), n=0..25); # Wesley Ivan Hurt, Jan 24 2014 MATHEMATICA Table[4 n! - 1, {n, 0, 25}] (* Vincenzo Librandi, Sep 30 2013 *) PROG (MAGMA) [4*Factorial(n)-1: n in [0..25]]; /* or */ [3] cat [n eq 1 select n+2 else n*Self(n-1)+n-1: n in [1..25] ]; // Vincenzo Librandi, Sep 30 2013 CROSSREFS Cf. sequences of the type k*n!-1: A033312 (k=1), A020543 (k=2), A173323 (k=3), this sequence, A173317 (k=5), A173316 (k=6). Cf. A002145 (Primes of the form 4*k+3). Sequence in context: A262375 A232368 A333924 * A191498 A065747 A232309 Adjacent sequences:  A173318 A173319 A173320 * A173322 A173323 A173324 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Feb 16 2010 STATUS approved

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Last modified September 23 08:47 EDT 2021. Contains 347611 sequences. (Running on oeis4.)