A287304 Primes that can be generated by the concatenation in base 5, in ascending order, of two consecutive integers read in base 10.

7, 13, 19, 131, 157, 313, 443, 521, 547, 599, 3529, 3907, 4159, 4663, 4789, 5167, 5419, 5923, 6301, 6427, 6553, 6679, 7057, 7309, 7561, 7687, 8191, 8317, 8443, 8821, 9199, 9829, 10333, 10459, 10711, 10837, 11467, 11593, 11719, 11971, 12097, 12601, 12853, 12979

Offset

1,1

Links

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

Example

1 and 2 in base 5 are 1 and 2 and concat(1,2) = 12 in base 10 is 7;
6 and 7 in base 5 are 11 and 12 and concat(11,12) = 1112 in base 10 is 157.

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, 5), i=1..1000);

Mathematica

With[{b = 5}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 120, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)
Select[FromDigits[Flatten[#], 5]&/@Partition[IntegerDigits[Range[150], 5], 2, 1], PrimeQ] (* Harvey P. Dale, Nov 25 2020 *)

Crossrefs

Cf. A000040, A030458.

Sequence in context: A355329 A133029 A243962 * A023984 A360400 A308200

Adjacent sequences: A287301 A287302 A287303 * A287305 A287306 A287307

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved