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Primes whose base-10 representation also represents a prime in base 17.
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%I #14 Apr 25 2017 15:40:58

%S 2,3,5,7,23,29,43,61,67,83,137,139,191,197,227,241,263,313,331,461,

%T 577,593,599,607,683,739,821,863,937,953,1013,1033,1039,1051,1297,

%U 1303,1327,1459,1619,1693,1721,1787,1811,1877,1949

%N Primes whose base-10 representation also represents a prime in base 17.

%C See A090713 for a similar sequence whose definition works "in the opposite direction".

%H Robert Israel, <a href="/A235126/b235126.txt">Table of n, a(n) for n = 1..10000</a>

%e The decimal representation of prime 23, considered as a number written in base 17, stands for 2*17+3 = 37, which is also prime, therefore 23 is in the sequence.

%p filter:= proc(p) local L;

%p if not isprime(p) then return false fi;

%p L:= convert(p,base,10);

%p isprime(add(L[i]*17^(i-1),i=1..nops(L)))

%p end proc:

%p select(filter, [2,seq(i,i=3..10000,2)]); # _Robert Israel_, Apr 25 2017

%t Select[Prime@ Range@ 300, PrimeQ@ FromDigits[IntegerDigits@ #, 17] &] (* _Michael De Vlieger_, Jan 03 2016 *)

%o (PARI) is(p, b=17)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows the production of similar sequences for other bases b > 9 (which can be given as an optional 2nd argument), but does not do the required check for bases b < 10.

%Y Cf. A235110 and other sequences in the range A090707 - A091924.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Jan 03 2014