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a(1) = prime(14), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).
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%I #18 Dec 16 2024 02:09:23

%S 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 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(14), for n >= 2, a(n) is the 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

%H Robert Israel, <a href="/A107814/b107814.txt">Table of n, a(n) for n = 1..10000</a>

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

%p Cands:= subsop(14=NULL, [seq(ithprime(i),i=1..1000)]):

%p S:= map(t -> convert(convert(t,base,10),set), Cands):

%p R:= 43: x:= 43: xs:= {3,4}:

%p for n from 2 to 100 do

%p found:= false;

%p for i from 1 do

%p if S[i] intersect xs <> {} then

%p R:= R, Cands[i];

%p x:= Cands[i];

%p xs:= S[i];

%p Cands:= subsop(i=NULL,Cands);

%p S:= subsop(i=NULL,S);

%p found:= true;

%p break

%p fi

%p od;

%p if not found then break fi;

%p od:

%p R; # _Robert Israel_, Dec 16 2024

%t 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 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), 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 nonn,base

%O 1,1

%A _Zak Seidov_ and _Eric Angelini_, May 24 2005