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

1,1

Links

Table of n, a(n) for n=1..39.

Example

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.

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 *)

Crossrefs

Cf. A000040, A030458.

Sequence in context: A081552 A364578 A156948 * A141915 A016133 A287833

Adjacent sequences: A287299 A287300 A287301 * A287303 A287304 A287305

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved