A287310 Primes that can be generated by the concatenation in base 8, in ascending order, of two consecutive integers read in base 10.

19, 37, 521, 911, 1171, 1301, 1951, 2081, 2341, 2731, 2861, 3121, 3251, 3511, 32833, 35911, 37963, 43093, 44119, 46171, 53353, 56431, 57457, 59509, 61561, 68743, 71821, 77977, 85159, 87211, 88237, 90289, 95419, 99523, 100549, 114913, 117991, 123121, 124147, 126199

Offset

1,1

Comments

Primes of the form (1+8^k) m + 1 where m+1 < 8^k < 8(m+1). - Robert Israel, May 24 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

2 and 3 in base 8 are 2_8 and 3_8, and concat(2,3) = 23_8 in base 10 is 19;
8 and 9 in base 8 are 10_8 and 11_8 and concat(10,11) = 1011_8 in base 10 is 521.

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

Mathematica

With[{b = 8}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 250, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 25 2017 *)

Crossrefs

Cf. A000040, A030458.

Sequence in context: A350469 A111441 A144594 * A123028 A067205 A196185

Adjacent sequences: A287307 A287308 A287309 * A287311 A287312 A287313

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 24 2017

Status

approved