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Beginning with 1, distinct numbers such that concatenation a(n+1), a(n), a(n+1) is a prime.
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%I #10 Jan 15 2025 04:16:58

%S 1,3,11,13,17,7,111,23,9,19,27,43,33,29,31,41,37,21,53,51,47,39,73,

%T 107,49,59,57,61,71,63,79,77,67,87,97,81,89,103,69,109,93,113,99,1019,

%U 123,131,117,101,1017,139,173,91,137,171,127,143,141,83,181,119,151,129,133

%N Beginning with 1, distinct numbers such that concatenation a(n+1), a(n), a(n+1) is a prime.

%C Conjecture: all positive integers coprime to 10 occur in the sequence. - _Robert Israel_, Jan 14 2025

%H Robert Israel, <a href="/A090260/b090260.txt">Table of n, a(n) for n = 1..10000</a>

%e 313,11311,131113 etc. are all primes.

%p aba:= proc(a,b) (a*10^(1+ilog10(b))+b)*10^(1+ilog10(a))+a end proc:

%p Cands:= remove(t -> t mod 5 = 0, [seq(i,i=3 .. 10^5,2)]):

%p R:= 1: x:= 1: nC:= nops(Cands):

%p for n from 2 to 100 do

%p found:= false:

%p for i from 1 to nC do

%p if isprime(aba(Cands[i],x)) then

%p found:= true;

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

%p x:= Cands[i];

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

%p nC:= nC-1;

%p break

%p fi

%p od;if not found then break fi;

%p od:

%p R; # _Robert Israel_, Jan 14 2025

%Y Cf. A090261.

%K base,nonn,look

%O 1,2

%A _Amarnath Murthy_, Nov 28 2003

%E More terms from _David Wasserman_, Apr 22 2004