many seqs need editing

[N. J. A. Sloane]

I also suggest Caldwell's site as relevant database.

Note that the given numbers are not arbitrary twins , but somehow of
palindromic nature : abcd 2^dcba + x
and in addition a,b,c,d are prime(1..4).

how about new sequence :

a(n) = smallest k such that m 2^m' + k is the lesser of a twin prime pair,
where m is concatenation of first n primes, and m' is m reversed.

gp > for(n=1,3,
t=2^sum(i=0,n-1,10^i*prime(i+1))*tt=sum(i=1,n,10^(n-i)*prime(i));
forstep(k=1,10^9,2,
if(!ispseudoprime(t+k)|!ispseudoprime(t+k+2),next);print([n,k,t]);next(2)))
[1, 3, 8]
[2, 393, 98784247808]
[3, 24031, 3303889817867659843626489216581892927607433821252970027433367373636818223305623904765545503857544848219473168746491907356106070384503626334115628335947854706114560]

so Jason's additional term  105525 would be the 4th in the sequence 3,393,24031

One could also replace the given m by 2n+1 (to avoid it ending in 0),
simply. then Jason's term would be the [2357/2]-th in the sequence:
5,19,123,29,13,993,59,... :

gp > for(n=1,20, if(9<t=2*n+1, t=(t\10)+(t%10)*10); t=(2*n+1)*2^t;
forstep(k=1,10^9,2,
if(!ispseudoprime(t+k)|!ispseudoprime(t+k+2),next);print([n,2*n+1,round(log(t/(2*n+1))/log(2)),k,t+k]);next(2)))
[1, 3, 3, 5, 29]
[2, 5, 5, 19, 179]
[3, 7, 7, 123, 1019]
[4, 9, 9, 29, 4637]
[5, 11, 11, 13, 22541]
[6, 13, 31, 993, 27917288417]
[7, 15, 51, 59, 33776997205278779]
[8, 17, 71, 2185, 40140115104391984318601]
[9, 19, 91, 759, 47041721492844450446166721271]
[10, 21, 12, 11, 86027]
[11, 23, 32, 393, 98784248201]
[12, 25, 52, 121, 112589990684262521]
[13, 27, 72, 1475, 127503895037480420771267]
[14, 29, 92, 1665, 143601044557104111888298411649]
[15, 31, 13, 87, 254039]
[16, 33, 33, 983, 283467842519]
[17, 35, 53, 421, 315251973915935141]
[18, 37, 73, 495, 349455119732353745813999]
[19, 39, 93, 413, 386237292257038645768526758301]
[20, 41, 14, 33, 671777]

Maximilian

On 6/3/07, Hugo Pfoertner <all at abouthugo.de> wrote:
> Jason Earls wrote:
> >
> > Dear Seqfans,
> >
> >  I recently found these twin probable primes:
> >
> >  2357*2^7532+105525
> > 2357*2^7532+105527
> > (2271 digits)
> >
> >  Anyone know of databases that keep track of these? They shouldn't be in the
> > OEIS, should they?
>
> Chris Caldwell maintains the authoritative list of biggest known primes;
> it includes also a section on twin primes.
> See http://primes.utm.edu/largest.html#twin or
> http://primes.utm.edu/primes/search.php?Number=200&Comment=Twin|Triplet
>
> Your examples are off by many orders of magnitude from the record zone.
> (the biggest currently known twin pair has 58711 digits)
>
> Hugo
>