A287301 Primes that can be generated by the concatenation in base 3, in descending order, of two consecutive integers read in base 10.

3, 7, 11, 59, 79, 89, 307, 419, 503, 587, 643, 727, 2377, 2459, 3361, 3607, 3853, 4099, 4591, 4673, 4919, 5657, 5821, 5903, 6067, 20983, 21227, 22447, 22691, 23911, 26107, 26839, 28547, 30011, 31231, 31963, 32939, 33427, 34159, 34403, 36599, 37087, 41479, 42943

Offset: 1

Author

Paolo P. Lava, May 23 2017

Keywords

• nonn
• base
• easy

Examples

			1 and 2 in base 3 are 1 and 2 and concat(2,1) = 21 in base 10 is 7;
2 and 3 in base 3 are 2 and 10 and concat(10,2) = 102 in base 10 is 11.
		

Crossrefs

Cf. A000040, A052089.

Programs

Maple

with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; if q=0 then 3 else 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; fi; end: seq(P(i,3),i=0..1000);

Mathematica

With[{b = 3}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 150], 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)