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

Author

Paolo P. Lava, May 24 2017

Keywords

• nonn
• base
• easy

Examples

			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.
		

Crossrefs

Cf. A000040, A030458.

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,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 *)