A163074
Swinging primes: primes which are within 1 of a swinging factorial (A056040).
Original entry on oeis.org
2, 3, 5, 7, 19, 29, 31, 71, 139, 251, 631, 3433, 12011, 48619, 51479, 51481, 2704157, 155117519, 280816201, 4808643121, 35345263801, 81676217699, 1378465288199, 2104098963721, 5651707681619, 94684453367401, 386971244197199, 1580132580471899, 1580132580471901
Offset: 1
3$ + 1 = 7 is prime, so 7 is in the sequence. (Here '$' denotes the swinging factorial function.)
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# Seq with arguments <= n:
a := proc(n) select(isprime,map(x -> A056040(x)+1,[$1..n]));
select(isprime,map(x -> A056040(x)-1,[$1..n]));
sort(convert(convert(%%,set) union convert(%,set),list)) end:
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Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f - 1], Sow[p]]; If[PrimeQ[p = f + 1], Sow[p]], {n, 1, 45}]][[2, 1]] // Union (* Jean-François Alcover, Jun 28 2013 *)
A163076
Primes of the form k$ - 1. Here '$' denotes the swinging factorial function (A056040).
Original entry on oeis.org
5, 19, 29, 139, 251, 12011, 48619, 51479, 155117519, 81676217699, 1378465288199, 5651707681619, 386971244197199, 1580132580471899, 30067266499541039, 6637553085023755473070799, 35257120210449712895193719, 399608854866744452032002440111
Offset: 1
Since 4$ = 6 the prime 5 is listed.
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a := proc(n) select(isprime, map(x -> A056040(x)-1,[$1..n])); sort(%) end:
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Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f - 1], Sow[p]], {n, 1, 70}]][[2, 1]] // Union (* Jean-François Alcover, Jun 28 2013 *)
A163083
Primes of the form k$ + 1 which are the greater of twin primes. Here '$' denotes the swinging factorial function (A056040).
Original entry on oeis.org
7, 31, 51481, 1580132580471901
Offset: 1
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a := proc(n) select(s->isprime(s) and isprime(s-2), map(k -> A056040(k)+1,[$4..n])) end:
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sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; Do[ If[ PrimeQ[p = sf[n] + 1] && PrimeQ[p - 2], Print["n = ", n, " p = ", p]], {n, 1, 400}] (* Jean-François Alcover, Jul 29 2013 *)
A163081
Primes of the form p$ + 1 where p is prime, where '$' denotes the swinging factorial (A056040).
Original entry on oeis.org
3, 7, 31, 4808643121, 483701705079089804581, 3283733939424401442167506310317720418331001
Offset: 1
3 and 3$ + 1 = 7 are prime, so 7 is a member.
Showing 1-4 of 4 results.
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