Help: A038537 and possible new seq

[Edwin Clark]

On Tue, 24 Jun 2003, David Wilson wrote:
> If a number n ends in 7 mod 10, it ends in 2 mod 5,
> so its mod 5 rep is even, and therefore nonprime.
> Hence n is not wonderful.
> 
> Why are there numbers ending in 7 in the list below?
> Why did Maple think their base-5 reps were prime?
> 

David:

SORRY! Not Maple's fault, but mine. I had a mistake in my program.
After correction the only wonderful numbers in Frank's list are:

                             50006393431
                             727533146383
                            2250332130313
                            2651541199513

But all of the 22 in Jack Brennen's list are wonderful --
assuming my new program is correct.

Here's my Maple procedure to check for wonderfulness.

> IsWonderful:=proc(x)
> local z,w,i,b;
> if not isprime(x) then return false; fi;
> for b from 2 to 9 do
> z:=convert(x,base,b);
> w:=add(z[i]*10^(i-1),i=1..nops(z));
> if not isprime(w) then return false; fi;
> od;
> return true;
> end proc:

[Note that convert(x,base,b) give the base b digits in reverse order--but
that wasn't my error. It was dumber. ]

I hope I have this straight now!

--Edwin

PS It wouldn't hurt if someone else also checked.
 
> 
> On Mon, 23 Jun 2003, Frank Ellermann wrote:
> 
> > Sorry, same problem here, but the 36 candidates are:
> > 
> > 50006393431
> > 153060758677
> > 564447201127
> > 727533146383
> > 2250332130313
> > 2515800864107
> > 2651541199513
> > 3420130221331
> > 7863444820201
> > 10344073503317
> > 12454426550417
> > 34550030320411
> > 40576217646011
> > 46453412755231
> > 103363643465221
> > 321403220334541
> > 362365443215623
> > 1304403114042211
> > 1314120224123011
> > 4441442135203001
> > 5350033510033241
> > 43404441441141013
> > 232210213100021113
> > 243332140011132223
> > 321420324021341023
> > 22211210112231010033
> > 200233302033310300021
> > 212211130022331222121
> > 11210002000211222202121
> > 2120112220000222011010021
> > 21222010111111220200020001
> > 100101111002110120010100121
> > 101110100100100111010000001001010111
> > 1010100101100100010110101101000100001111
> > 100000101111110010001111110100110000001001
> > 100110100101011100001010111101101010011001
> > 
>