A107801 a(1) = prime(1), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

2, 23, 3, 13, 11, 17, 7, 37, 31, 19, 29, 59, 5, 53, 43, 41, 47, 67, 61, 71, 73, 79, 89, 83, 103, 101, 107, 97, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset: 1

Author

Zak Seidov & Eric Angelini, May 24 2005

Keywords

• nonn
• base

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. If it exists, N > 10^1000. - Charles R Greathouse IV, Jul 19 2011

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A107353.

Other cases of seed: A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107808 (a(1) = 19), A107809 (a(1) = 23), A107810 (a(1) = 29), A107811 (a(1) = 31), A107812 (a(1) = 37), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

Haskell

import Data.List (intersect, delete)
a107801 n = a107801_list !! (n-1)
a107801_list = 2 : f 2 (tail a000040_list) where
   f x ps = g ps where
     g (q:qs) | null (show x `intersect` show q) = g qs
              | otherwise                        = q : f q (delete q ps)
-- Reinhard Zumkeller, Mar 31 2012

Mathematica

p=Prime[1];b={p};d=p;Do[Do[r=Prime[c];If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r];d=r;Break[]], {c, 1000}], {k, 60}];b

PARI

common(a,b)=a=vecsort(eval(Vec(Str(a))),,8);b=vecsort(eval(Vec(Str(b))),,8);#a+#b>#vecsort(concat(a,b),,8)
in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0
lista(nn) = {my(v=[2]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v,p)&&common(v[#v],p), v=concat(v,p); break))); v; }
\\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 19 2011

For n>=29, A(107800+i)(n) = A(107800+j)(n), 1 <= i < j <= 14. - Vladimir Shevelev, Mar 18 2012