A287303 Primes that can be generated by the concatenation in base 4, in descending order, of two consecutive integers read in base 10.

19, 101, 271, 1429, 1559, 1949, 2339, 2729, 3119, 3769, 4159, 17989, 18503, 19531, 21587, 24671, 27241, 29297, 30839, 32381, 33409, 33923, 36493, 44203, 47287, 51913, 55511, 64763, 286999, 289049, 293149, 295199, 301349, 305449, 323899, 332099, 336199, 350549, 375149

Offset: 1

Author

Paolo P. Lava, May 23 2017

Keywords

• nonn
• base
• easy

Examples

			3 and 4 in base 4 are 3 and 10 and concat(10,3) = 103 in base 10 is 19;
5 and 6 in base 4 are 11 and 12 and concat(12,11) = 1211 in base 10 are 101.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A052089.

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] &, Reverse /@ Partition[Range[0, 370], 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)
Select[Table[FromDigits[Join[IntegerDigits[n+1,4],IntegerDigits[n,4]],4],{n,1000}],PrimeQ] (* Harvey P. Dale, Dec 28 2024 *)