A287300 Primes that can be generated by the concatenation in base 3, in ascending order, of two consecutive integers read in base 10.

5, 31, 41, 61, 71, 281, 337, 421, 449, 617, 673, 701, 2297, 2543, 2707, 2789, 2953, 3527, 3691, 4019, 5003, 5167, 5413, 5659, 5741, 5987, 6151, 6397, 21961, 22937, 23669, 24889, 25621, 26597, 27329, 27817, 28549, 28793, 30013, 31477, 31721, 32941, 34649, 35381

Offset: 1

Author

Paolo P. Lava, May 23 2017

Keywords

• nonn
• base
• easy

Examples

			1 and 2 in base 3 are 1 and 2 and concat(1,2) = 12 in base 10 is 5;
3 and 4 in base 3 are 10 and 11 and concat(10,11) = 1011 in base 10 is 31.
		

Crossrefs

Cf. A000040, A030458.

Programs

Maple

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,3),i=1..1000);

Mathematica

With[{b = 3}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 150, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)