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

1,1

Links

Table of n, a(n) for n=1..44.

Example

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.

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 *)

Crossrefs

Cf. A000040, A030458.

Sequence in context: A027761 A166306 A341632 * A162665 A130474 A238674

Adjacent sequences: A287297 A287298 A287299 * A287301 A287302 A287303

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved