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A107814 a(1) = prime(14), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

%I A107814 #18 Dec 16 2024 02:09:23
%S A107814 43,3,13,11,17,7,37,23,2,29,19,31,41,47,67,61,71,73,53,5,59,79,89,83,
%T A107814 103,101,107,97,109,113,127,131,137,139,149,151,157,163,167,173,179,
%U A107814 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277
%N A107814 a(1) = prime(14), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).
%C A107814 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
%H A107814 Robert Israel, <a href="/A107814/b107814.txt">Table of n, a(n) for n = 1..10000</a>
%F A107814 a(n) ~ n log n. - _Charles R Greathouse IV_, Jul 20 2011
%p A107814 Cands:= subsop(14=NULL, [seq(ithprime(i),i=1..1000)]):
%p A107814 S:= map(t -> convert(convert(t,base,10),set), Cands):
%p A107814 R:= 43: x:= 43: xs:= {3,4}:
%p A107814 for n from 2 to 100 do
%p A107814   found:= false;
%p A107814   for i from 1 do
%p A107814     if S[i] intersect xs <> {} then
%p A107814       R:= R, Cands[i];
%p A107814       x:= Cands[i];
%p A107814       xs:= S[i];
%p A107814       Cands:= subsop(i=NULL,Cands);
%p A107814       S:= subsop(i=NULL,S);
%p A107814       found:= true;
%p A107814       break
%p A107814     fi
%p A107814   od;
%p A107814   if not found then break fi;
%p A107814 od:
%p A107814 R; # _Robert Israel_, Dec 16 2024
%t A107814 p=Prime[14];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
%Y A107814 Cf. A107353.
%Y A107814 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), A107813 (a(1) = 41).
%K A107814 nonn,base
%O A107814 1,1
%A A107814 _Zak Seidov_ and _Eric Angelini_, May 24 2005