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A107808 a(1)=prime(8), for n>=2 a(n) = smallest prime not previously used which contains a digit from a(n-1). 14

%I

%S 19,11,13,3,23,2,29,59,5,53,31,17,7,37,43,41,47,67,61,71,73,79,89,83,

%T 103,101,107,97,109,113,127,131,137,139,149,151,157,163,167,173,179,

%U 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277

%N a(1)=prime(8), for n>=2 a(n) = smallest prime not previously used which contains a digit from a(n-1).

%C 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. [_Charles R Greathouse IV_, Jul 20 2011]

%F a(n) ~ n log n. [_Charles R Greathouse IV_, Jul 20 2011]

%t p=Prime[8];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

%o (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)

%o in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0

%o v=[19];for(n=2,1000,forprime(p=2,default(primelimit),if(!in(p,v)&&common(v[#v],p),v=concat(v,p);break))); v

%o \\ _Charles R Greathouse IV_, Jul 20 2011

%Y Cf. A107353.

%Y Other cases of seed: A107801 a(1)=2, A107802 a(1)=3, A107803 a(1)=5, A107804 a(1)=7, A107805 a(1)=11, A107806 a(1)=13, A107807 a(1)=17, A107809 a(1)=23, A107810 a(1)=29, A107811 a(1)=31, A107812 a(1)=37, A107813 a(1)=41, A107814 a(1)=43

%K base,nonn

%O 1,1

%A _Zak Seidov_ & _Eric Angelini_, May 24 2005

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Last modified February 21 20:28 EST 2020. Contains 332111 sequences. (Running on oeis4.)