A287313 Primes that can be generated by the concatenation in base 9, in descending order, of two consecutive integers read in base 10.
19, 29, 59, 79, 89, 983, 1229, 1721, 2131, 2213, 2377, 2459, 3361, 3607, 3853, 4099, 4591, 4673, 4919, 5657, 5821, 5903, 6067, 60589, 64969, 65699, 70079, 72269, 76649, 78839, 83219, 86869, 91249, 94169, 95629, 102199, 102929, 107309, 108769, 113149, 117529, 118259
Offset: 1
Examples
1 and 2 in base 9 are 1 and 2 and concat(21) = 21 in base 10 is 19; 8 and 9 in base 9 are 8 and 10 and concat(10,8) = 108 in base 10 is 89.
Programs
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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=0..1000);
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Mathematica
With[{b = 9}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Reverse /@ Partition[Range[0, 165], 2, 1]], PrimeQ]] (* Michael De Vlieger, May 25 2017 *)