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a(n) is the first number that starts a sequence of exactly n primes x(1), ..., x(n) where x(i+1) = A004093(x(i)) is the digit reversal of 2 * x(i).
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%I #9 Jun 23 2024 22:04:31

%S 2,7,19,487,1637,389047

%N a(n) is the first number that starts a sequence of exactly n primes x(1), ..., x(n) where x(i+1) = A004093(x(i)) is the digit reversal of 2 * x(i).

%C a(7) > 7 * 10^9 if it exists.

%e a(1) = 2 because 2 is prime while A004093(2) = 4 is not prime.

%e a(2) = 7 because 7 and A004093(7) = 41 are prime but A004093(41) = 28 is not.

%e a(3) = 19 because 19 and A004093(19) = 83 and A004093(83) = 661 are prime but A004093(661) = 2231 is not.

%p g:= proc(n) local t,L,i,j;

%p t:= n;

%p for i from 0 while isprime(t) do

%p L:= convert(2*t,base,10);

%p t:= add(L[-j]*10^(j-1),j=1..nops(L));

%p od;

%p i

%p end proc:

%p V:= Vector(6): count:= 0: p:= 1:

%p while count < 6 do

%p p:= nextprime(p); v:= g(p);

%p if V[v] = 0 then V[v]:= p; count:= count+1 fi

%p od:

%p convert(V,list);

%Y Cf. A004093.

%K nonn,base,more

%O 1,1

%A _Robert Israel_, Jun 18 2024