A139074 or 0 if no such prime exists.

[N. J. A. Sloane]

Dear Neil,
Mayby we don't understand one other.
If in title you will be change on
a(n) = smallest prime p such that (n+p!)/n is prime
and all will be as good as this is possible in this case

without  "or 0 if no such prime exists."

because we can't put zero without proof which can't exist recently that 
after deleting "or 0 if no such prime exists."
all will be prefect.

BEST WISHES
ARTUR


N. J. A. Sloane pisze:
> Concerning the question of
>
> avs> Good: a(n) = 0 if no such prime exists
> avs> Bad: a(n) = 0 if no such prime is known
>
> , I totally agree!  The OEIS should
> not have definitions which says things
> like "as far as is known today".
>
> There are some exceptions, in the case of very important sequences.
>
> But if the next term in a sequence is not known,
> then the rule is that the entry ends at that point.
>
>
>  Best regards
>  			 Neil
>
> __________ NOD32 Informacje 2701 (20071204) __________
>
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>
>   




aj> From seqfan-owner at ext.jussieu.fr  Wed Apr 23 17:47:33 2008
aj> Date: Wed, 23 Apr 2008 17:49:24 +0200
aj> From: Artur <grafix at csl.pl>
aj> Reply-To: grafix at csl.pl
aj> To: "N. J. A. Sloane" <njas at research.att.com>
aj> CC: seqfan <seqfan at ext.jussieu.fr>
aj> Subject: Proof
aj> ...
aj> I hope that I have proof:
aj> 1) 4 x^2 - 4 x*y + 7 y^2 can be odd prime only  if y is odd
aj> 4 x^2 - 4 x*(2 k + 1) + 7 (2 k + 1)^2=7 + 28 k + 28 k^2 - 4 x - 8 k x + 
aj> 4 x^2=
aj> 7+4(7 k + 7 k^2 - x - 2 k x + x^2)
aj> 2) Now if we solve equation (7 k + 7 k^2 - x - 2 k x + x^2) = m on 
aj> variable x and we will be forced x as positive integer
aj> we are receiving
aj> x=(1+2k+/-Sqrt[-24k^2-24k+4m+1])/2
aj> now to integer x condition need     -24k^2-24k+4m+1 have to be odd square
aj> but these have to be 24w+1 as Zak Seidov states in comment to A001318 
aj> <http://www.research.att.com/%7Enjas/sequences/A001318>
...

This is not clear to me: the -24k^2-24k+4m+1 can be odd squares without
being of the form 24w+1: they can (at least) also be of the form 24w+8 :

"k=", 2, "m=", 48, "-24k^2-24k+4m+1=", 49, "-24*k^2-24*k+4*m=", 48, "mod 24", 0

"k=", 2, "m=", 56, "-24k^2-24k+4m+1=", 81, "-24*k^2-24*k+4*m=", 80, "mod 24", 8

"k=", 2, "m=", 66, "-24k^2-24k+4m+1=", 121, "-24*k^2-24*k+4*m=", 120, "mod 24", 0

"k=", 2, "m=", 78, "-24k^2-24k+4m+1=", 169, "-24*k^2-24*k+4*m=", 168, "mod 24", 0

"k=", 2, "m=", 92, "-24k^2-24k+4m+1=", 225, "-24*k^2-24*k+4*m=", 224, "mod 24", 8

"k=", 3, "m=", 72, "-24k^2-24k+4m+1=", 1, "-24*k^2-24*k+4*m=", 0, "mod 24", 0

"k=", 3, "m=", 74, "-24k^2-24k+4m+1=", 9, "-24*k^2-24*k+4*m=", 8, "mod 24", 8

"k=", 3, "m=", 78, "-24k^2-24k+4m+1=", 25, "-24*k^2-24*k+4*m=", 24, "mod 24", 0

"k=", 3, "m=", 84, "-24k^2-24k+4m+1=", 49, "-24*k^2-24*k+4*m=", 48, "mod 24", 0

"k=", 3, "m=", 92, "-24k^2-24k+4m+1=", 81, "-24*k^2-24*k+4*m=", 80, "mod 24", 8

Experimental scanner in Maple:
for k from -100 to 100 do
od: