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

1,1

Links

Table of n, a(n) for n=1..44.

Example

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.

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 *)

Crossrefs

Cf. A000040, A052089.

Sequence in context: A005372 A125220 A016081 * A105762 A057469 A247229

Adjacent sequences: A287298 A287299 A287300 * A287302 A287303 A287304

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved