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A287305 Primes that can be generated by the concatenation in base 5, in descending order, of two consecutive integers read in base 10.

%I A287305 #8 May 24 2017 09:13:51
%S A287305 5,11,17,23,29,181,233,311,337,389,467,571,3527,3779,4157,4283,4409,
%T A287305 4787,5039,5417,5669,6047,6173,6299,6551,6803,7307,7433,7559,7937,
%U A287305 8693,8819,9323,10079,10331,10457,10709,11087,11213,11717,11969,12347,12473,13103,13229
%N A287305 Primes that can be generated by the concatenation in base 5, in descending order, of two consecutive integers read in base 10.
%e A287305 1 and 2 in base 5 are 1 and 2 and concat(2,1) = 21 in base 10 is 11;
%e A287305 6 and 7 in base 5 are 11 and 12 and concat(1211) = 1211 in base 10 is 181.
%p A287305 with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; if q=0 then 5 else 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; fi; end: seq(P(i,5),i=0..1000);
%t A287305 With[{b = 5}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 108], 2, 1]], PrimeQ]] (* _Michael De Vlieger_, May 23 2017 *)
%Y A287305 Cf. A000040, A052089.
%K A287305 nonn,base,easy
%O A287305 1,1
%A A287305 _Paolo P. Lava_, May 23 2017