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%I #8 May 24 2017 09:13:07
%S 3,7,11,59,79,89,307,419,503,587,643,727,2377,2459,3361,3607,3853,
%T 4099,4591,4673,4919,5657,5821,5903,6067,20983,21227,22447,22691,
%U 23911,26107,26839,28547,30011,31231,31963,32939,33427,34159,34403,36599,37087,41479,42943
%N Primes that can be generated by the concatenation in base 3, in descending order, of two consecutive integers read in base 10.
%e 1 and 2 in base 3 are 1 and 2 and concat(2,1) = 21 in base 10 is 7;
%e 2 and 3 in base 3 are 2 and 10 and concat(10,2) = 102 in base 10 is 11.
%p with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; if q=0 then 3 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,3),i=0..1000);
%t With[{b = 3}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 150], 2, 1]], PrimeQ]] (* _Michael De Vlieger_, May 23 2017 *)
%Y Cf. A000040, A052089.
%K nonn,base,easy
%O 1,1
%A _Paolo P. Lava_, May 23 2017
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