A287309 Primes that can be generated by the concatenation in base 7, in descending order, of two consecutive integers read in base 10.

7, 23, 31, 47, 449, 499, 599, 1049, 1249, 1399, 1499, 1549, 1699, 1949, 1999, 2099, 2399, 18919, 20639, 20983, 24767, 25111, 25799, 29927, 30271, 31991, 33023, 38183, 40591, 45751, 46439, 48847, 51599, 52631, 57791, 59167, 60887, 61231, 64327, 66047, 67079, 68111

Offset: 1

Author

Paolo P. Lava, May 23 2017

Keywords

• nonn
• base
• easy

Examples

			2 and 3 in base 7 are 2 and 3 and concat(3,2) = 32 in base 10 is 23;
8 and 9 in base 7 are 11 and 12 and concat(12,11) = 1211 in base 10 is 449.
		

Crossrefs

Cf. A000040, A052089.

Programs

Maple

with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; if q=0 then 7 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,7),i=0..1000);

Mathematica

With[{b = 7}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 200], 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)