A287310 - OEIS

%I #21 Jun 17 2021 04:44:47

%S 19,37,521,911,1171,1301,1951,2081,2341,2731,2861,3121,3251,3511,

%T 32833,35911,37963,43093,44119,46171,53353,56431,57457,59509,61561,

%U 68743,71821,77977,85159,87211,88237,90289,95419,99523,100549,114913,117991,123121,124147,126199

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

%C Primes of the form (1+8^k) m + 1 where m+1 < 8^k < 8(m+1). - _Robert Israel_, May 24 2017

%H Robert Israel, <a href="/A287310/b287310.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 and 3 in base 8 are 2_8 and 3_8, and concat(2,3) = 23_8 in base 10 is 19;

%e 8 and 9 in base 8 are 10_8 and 11_8 and concat(10,11) = 1011_8 in base 10 is 521.

%p 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);

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

%Y Cf. A000040, A030458.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, May 24 2017