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A107813 a(1) = prime(13), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

%I A107813 #13 Apr 11 2020 10:40:38
%S A107813 41,11,13,3,23,2,29,19,17,7,37,31,43,47,67,61,71,73,53,5,59,79,89,83,
%T A107813 103,101,107,97,109,113,127,131,137,139,149,151,157,163,167,173,179,
%U A107813 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277
%N A107813 a(1) = prime(13), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).
%C A107813 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 A107813 a(n) ~ n log n. - _Charles R Greathouse IV_, Jul 20 2011
%t A107813 p=Prime[13];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 A107813 (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 A107813 in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0
%o A107813 lista(nn) = {my(v=[41]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v,p)&&common(v[#v],p), v=concat(v,p); break))); v; }
%o A107813 \\ _Charles R Greathouse IV_, Jul 20 2011
%Y A107813 Cf. A107353.
%Y A107813 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), A107808 (a(1) = 19), A107809 (a(1) = 23), A107810 (a(1) = 29), A107811 (a(1) = 31), A107812 (a(1) = 37), A107814 (a(1) = 43).
%K A107813 nonn,base
%O A107813 1,1
%A A107813 _Zak Seidov_ and _Eric Angelini_, May 24 2005