A287312 Primes that can be generated by the concatenation in base 9, in ascending order, of two consecutive integers read in base 10.

11, 31, 41, 61, 71, 739, 821, 1231, 1559, 1723, 2297, 2543, 2707, 2789, 2953, 3527, 3691, 4019, 5003, 5167, 5413, 5659, 5741, 5987, 6151, 6397, 65701, 66431, 67891, 72271, 76651, 81031, 81761, 83221, 85411, 100741, 102931, 108041, 121181, 135781, 136511, 140891

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Example

1 and 2 in base 9 are 1 and 2 and concat(1,2) = 12 in base 10 is 11;
9 and 10 in base 9 are 10 and 11 and concat(10,11) = 1011 in base 10 is 739.

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

Mathematica

With[{b = 9}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 200, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 25 2017 *)

Crossrefs

Cf. A000040, A030458.

Sequence in context: A040979 A181182 A089347 * A240896 A040985 A061599

Adjacent sequences: A287309 A287310 A287311 * A287313 A287314 A287315

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 24 2017

Status

approved