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Primes that can be generated by the concatenation in base 6, in ascending order, of two consecutive integers read in base 10.
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%I #8 May 24 2017 09:14:00

%S 29,223,593,1259,8681,11719,14323,16493,16927,18229,19531,20399,21701,

%T 23003,26041,28211,29947,31249,32117,34721,36457,39929,41231,42533,

%U 42967,44269,45137,46439,293123,316469,324251,350191,355379,363161,381319,396883,402071,425417

%N Primes that can be generated by the concatenation in base 6, in ascending order, of two consecutive integers read in base 10.

%e 4 and 5 in base 6 are 4 and 5 and concat(4,5) = 45 in base 10 is 29;

%e 6 and 7 in base 6 are 10 and 11 and concat(10,11) = 1011 in base 10 is 223.

%p with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; a:=convert(q+1,base,h); b:=convert(q,base,h); c:=[op(a),op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; end: seq(P(i,6),i=1..1000);

%t With[{b = 6}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 360, 2, 1]], PrimeQ]] (* _Michael De Vlieger_, May 23 2017 *)

%Y Cf. A000040, A030458.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, May 23 2017