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

1,1

Links

Table of n, a(n) for n=1..42.

Example

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.

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 *)

Crossrefs

Cf. A000040, A052089.

Sequence in context: A007522 A141175 A295196 * A275777 A329931 A157811

Adjacent sequences: A287306 A287307 A287308 * A287310 A287311 A287312

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved