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A163074 Swinging primes: primes which are within 1 of a swinging factorial (A056040). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Union of A163075 and A163076.

REFERENCES

Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.

LINKS

Table of n, a(n) for n=1..26.

Peter Luschny, Swinging Primes.

EXAMPLE

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

MAPLE

# 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:

MATHEMATICA

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-Fran├žois Alcover, Jun 28 2013 *)

CROSSREFS

Cf. A088054, A163075, A163076.

Sequence in context: A244529 A025019 A140327 * A230041 A068803 A184902

Adjacent sequences:  A163071 A163072 A163073 * A163075 A163076 A163077

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 21 2009

STATUS

approved

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Last modified December 21 18:59 EST 2014. Contains 252325 sequences.