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%I #14 Nov 02 2023 14:18:28
%S 2,3,5,7,23,29,43,47,113,131,151,157,179,199,229,263,283,311,317,353,
%T 359,409,421,443,461,557,593,641,661,739,773,809,821,881,937,953,977,
%U 1031,1109,1213,1217,1231,1279,1291,1297,1307,1433,1439,1583,1657,1693,1697,1741,1789,1811,1873,1877,1949,1987,2003
%N Primes whose base-10 representation also represents a prime in base 19.
%C See A090714 for a similar sequence whose definition works "in the opposite direction".
%H Robert Price, <a href="/A235144/b235144.txt">Table of n, a(n) for n = 1..3276</a>
%e The decimal representation of prime 23, considered as a number written in base 19, stands for 2*19 + 3 = 41, which is also prime, therefore 23 is in the sequence.
%t Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#], 19]] &] (* _Alonso del Arte_, Jan 04 2014 *)
%o (PARI) is_A235144(p, b=19)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows one to produce similar sequences for other bases b > 9 (which can be given as optional 2nd argument), but does not do the required check for bases b < 10.
%Y Cf. A235110, A235126 and other sequences in the range A090707 - A091924.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Jan 03 2014