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A119555
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Primes in the sequence f(n) = f(n-1)+((-1)^n)*n!, with f(0)=0.
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0
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19, 619, 35899, 3301819, 468544077492065936712052044718939948687543330546977719976017418129955876663406131164377030450551575840099843957105136480237871017419158043635450756712088769133544426722033165168878328322819566779381528981882285541609256481166622331374702000809600061055686236758821446539362161635577019
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OFFSET
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1,1
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COMMENTS
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f(n) = (-1)^n*A005165(n). The primes are those terms in A071828 which correspond to even n values in A001272: n = 4, 6, 8, 10, 160, 4998, 9158, 11164 (the last three are only probable primes). 3612703 divides f(n) for n >= 3612702, so the sequence is finite. - Jens Kruse Andersen, Jul 04 2014
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REFERENCES
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G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 160.
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LINKS
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EXAMPLE
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f(0)=0, f(1) = 0+((-1)^1)*1! = -1, f(2) = -1+((-1)^2)*2! = 1, f(3) = 1+((-1)^3)*3! = -5, f(4) = -5+((-1)^4)*4! = 19, which is prime, so 19 is the first term of the sequence.
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MAPLE
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P:=proc(n) local i, j; j:=0; for i from 1 by 1 to n do j:=j+((-1)^i)*i!; if isprime(j) then print(j); fi; od; end: P(100);
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, a+(-1)^(n+1) (n+1)!}; Select[NestList[nxt, {0, 0}, 200][[All, 2]], #>0&&PrimeQ[#]&] (* Harvey P. Dale, Jan 22 2017 *)
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CROSSREFS
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KEYWORD
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nonn,fini
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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