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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A052089.

Sequence in context: A241236 A044270 A044651 * A142216 A027005 A061696

Adjacent sequences: A287300 A287301 A287302 * A287304 A287305 A287306

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved