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A163074 Swinging primes: primes which are within 1 of a swinging factorial (A056040). 5

%I #11 May 08 2020 17:37:35

%S 2,3,5,7,19,29,31,71,139,251,631,3433,12011,48619,51479,51481,2704157,

%T 155117519,280816201,4808643121,35345263801,81676217699,1378465288199,

%U 2104098963721,5651707681619,94684453367401,386971244197199,1580132580471899,1580132580471901

%N Swinging primes: primes which are within 1 of a swinging factorial (A056040).

%C Union of A163075 and A163076.

%H Jinyuan Wang, <a href="/A163074/b163074.txt">Table of n, a(n) for n = 1..103</a>

%H Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.

%H Peter Luschny, <a href="http://www.luschny.de/math/primes/SwingingPrimes.html"> Swinging Primes.</a>

%e 3$ + 1 = 7 is prime, so 7 is in the sequence. (Here '$' denotes the swinging factorial function.)

%p # Seq with arguments <= n:

%p a := proc(n) select(isprime,map(x -> A056040(x)+1,[$1..n]));

%p select(isprime,map(x -> A056040(x)-1,[$1..n]));

%p sort(convert(convert(%%,set) union convert(%,set),list)) end:

%t Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f - 1], Sow[p]]; If[PrimeQ[p = f + 1], Sow[p]], {n, 1, 45}]][[2, 1]] // Union (* _Jean-François Alcover_, Jun 28 2013 *)

%Y Cf. A088054, A163075, A163076.

%K nonn

%O 1,1

%A _Peter Luschny_, Jul 21 2009

%E More terms from _Jinyuan Wang_, Mar 22 2020

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)