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A130309
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Primes of the form [k!! - (k-1)!! + (k-2)!! -....1!!] + 1.
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2
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OFFSET
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1,1
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COMMENTS
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The next term is too large to include.
The corresponding values of k are 1, 2, 3, 4, 7, 31, 63, 263, 311, 371, 383, 10243, ... (1 and 2 give the same prime, 2). All these values except 2 and 4 are odd since for k even above 10 this form is divisible by 7. a(11) ~ 2.060 * 10^18317. - Amiram Eldar, Jul 18 2019
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LINKS
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EXAMPLE
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2 = 1!! + 1 or 2!! - 1!! + 1.
7 = 4!! - 3!! + 2!! - 1!! +1 = 8 - 3 + 2 - 1 + 1.
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MAPLE
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P:=proc(n) local a, i, j, k, w; for i from 1 by 1 to n do a:=0; for j from i by -1 to 0 do k:=j; w:=j-2; while w>0 do k:=k*w; w:=w-2; od; a:=a+k*(-1)^j od; if isprime(abs(a)+1) then print(abs(a)+1); fi; od; end: P(1000);
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MATHEMATICA
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f[n_] := Sum[(-1)^(n-k)*k!!, {k, 1, n}] + 1; Select[f/@Range[2, 31], PrimeQ] (* Amiram Eldar, Jul 18 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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