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A287309 Primes that can be generated by the concatenation in base 7, in descending order, of two consecutive integers read in base 10.

%I A287309 #8 May 24 2017 09:14:23
%S A287309 7,23,31,47,449,499,599,1049,1249,1399,1499,1549,1699,1949,1999,2099,
%T A287309 2399,18919,20639,20983,24767,25111,25799,29927,30271,31991,33023,
%U A287309 38183,40591,45751,46439,48847,51599,52631,57791,59167,60887,61231,64327,66047,67079,68111
%N A287309 Primes that can be generated by the concatenation in base 7, in descending order, of two consecutive integers read in base 10.
%e A287309 2 and 3 in base 7 are 2 and 3 and concat(3,2) = 32 in base 10 is 23;
%e A287309 8 and 9 in base 7 are 11 and 12 and concat(12,11) = 1211 in base 10 is 449.
%p A287309 with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; if q=0 then 7 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,7),i=0..1000);
%t A287309 With[{b = 7}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 200], 2, 1]], PrimeQ]] (* _Michael De Vlieger_, May 23 2017 *)
%Y A287309 Cf. A000040, A052089.
%K A287309 nonn,base,easy
%O A287309 1,1
%A A287309 _Paolo P. Lava_, May 23 2017