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

Author

Paolo P. Lava, May 24 2017

Keywords

• nonn
• base
• easy

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A030458.

Programs

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 *)