A287302 Primes that can be generated by the concatenation in base 4, in ascending order, of two consecutive integers read in base 10.

11, 103, 137, 239, 1171, 1301, 1951, 2081, 2341, 2731, 2861, 3121, 3251, 3511, 16963, 17477, 20047, 21589, 23131, 26729, 30841, 34439, 40093, 43177, 43691, 45233, 46261, 60139, 61681, 63737, 270601, 272651, 278801, 291101, 295201, 297251, 315701, 321851, 325951

Offset: 1

Author

Paolo P. Lava, May 23 2017

Keywords

• nonn
• base
• easy

Examples

			2 and 3 in base 4 are 2 and 3 and concat(2,3) = 23 in base 10 is 11;
6 and 7 in base 4 are 12 and 13 and concat(12,13) = 1213 in base 10 is 103.
		

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

Mathematica

With[{b = 4}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 320, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)