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A287304 Primes that can be generated by the concatenation in base 5, in ascending order, of two consecutive integers read in base 10.

%I A287304 #10 Nov 25 2020 19:24:50
%S A287304 7,13,19,131,157,313,443,521,547,599,3529,3907,4159,4663,4789,5167,
%T A287304 5419,5923,6301,6427,6553,6679,7057,7309,7561,7687,8191,8317,8443,
%U A287304 8821,9199,9829,10333,10459,10711,10837,11467,11593,11719,11971,12097,12601,12853,12979
%N A287304 Primes that can be generated by the concatenation in base 5, in ascending order, of two consecutive integers read in base 10.
%e A287304 1 and 2 in base 5 are 1 and 2 and concat(1,2) = 12 in base 10 is 7;
%e A287304 6 and 7 in base 5 are 11 and 12 and concat(11,12) = 1112 in base 10 is 157.
%p A287304 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,5),i=1..1000);
%t A287304 With[{b = 5}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 120, 2, 1]], PrimeQ]] (* _Michael De Vlieger_, May 23 2017 *)
%t A287304 Select[FromDigits[Flatten[#],5]&/@Partition[IntegerDigits[Range[150],5],2,1],PrimeQ] (* _Harvey P. Dale_, Nov 25 2020 *)
%Y A287304 Cf. A000040, A030458.
%K A287304 nonn,base,easy
%O A287304 1,1
%A A287304 _Paolo P. Lava_, May 23 2017