A287307 Primes that can be generated by the concatenation in base 6, in descending order, of two consecutive integers read in base 10.

13, 41, 443, 739, 887, 1109, 9547, 11717, 14321, 16057, 17359, 18661, 19963, 22133, 22567, 23869, 25171, 28643, 29077, 31247, 32983, 33851, 35153, 40361, 43399, 44267, 44701, 45569, 287933, 290527, 303497, 306091, 311279, 319061, 337219, 345001, 389099, 391693

Offset: 1

Author

Paolo P. Lava, May 23 2017

Keywords

• nonn
• base
• easy

Examples

			1 and 2 in base 6 are 1 and 2 and concat(2,1) = 21 in base 10 is 13;
5 and 6 in base 6 are 5 and 10 and concat(10,5) = 105 in base 10 is 41.
		

Crossrefs

Cf. A000040, A052089.

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,6),i=0..1000);

Mathematica

With[{b = 6}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 302], 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)