cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A163078 Numbers k such that k$ - 1 is prime. Here '$' denotes the swinging factorial function (A056040).

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%I A163078 #11 May 08 2020 17:43:21
%S A163078 3,4,5,6,7,10,13,15,18,30,35,39,41,47,49,58,83,86,102,111,137,151,195,
%T A163078 205,226,229,317,319,321,368,389,426,444,477,534,558,567,738,804,882,
%U A163078 1063,1173,1199,1206,1315,1624,1678,1804,2371,2507,2541,2844,3084,3291
%N A163078 Numbers k such that k$ - 1 is prime. Here '$' denotes the swinging factorial function (A056040).
%H A163078 Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.
%H A163078 Peter Luschny, <a href="http://www.luschny.de/math/primes/SwingingPrimes.html"> Swinging Primes.</a>
%e A163078 4$ - 1 = 6 - 1 = 5 is prime, so 4 is in the sequence.
%p A163078 a := proc(n) select(x -> isprime(A056040(x)-1),[$0..n]) end:
%t A163078 fQ[n_] := PrimeQ[ -1 + 2^(n - Mod[n, 2])*Product[k^((-1)^(k + 1)), {k, n}]]; Select[ Range@ 3647, fQ] (* _Robert G. Wilson v_, Aug 09 2010 *)
%o A163078 (PARI) is(k) = ispseudoprime(k!/(k\2)!^2-1); \\ _Jinyuan Wang_, Mar 22 2020
%Y A163078 Cf. A002982, A056040, A163077, A163079, A163080.
%K A163078 nonn
%O A163078 1,1
%A A163078 _Peter Luschny_, Jul 21 2009
%E A163078 a(42)-a(54) from _Robert G. Wilson v_, Aug 09 2010