|
%I #24 Jun 29 2019 02:03:39
%S 673,1165921,6228961,53378329,128818873,805379161,926711449,
%T 1542173569,2459671993,8365652929,14232980953,26484614209,30755887321,
%U 31937961241,37968797689,78180076129,80974979329,97835803129,168394504129,314911422913,410879716321,529074406681
%N Primes whose base-4 representation is a square when read in base 10.
%C Primes in the sequence A267764.
%H Chai Wah Wu, <a href="/A267818/b267818.txt">Table of n, a(n) for n = 1..100</a>
%e 673 written in base 4 is 22201, and 22201 in base 10 is 149^2.
%t Select[Prime@ Range[10^6], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 4] &] (* _Michael De Vlieger_, Jan 24 2016 *)
%o (PARI) is(n, b=4, c=10)=issquare(subst(Pol(digits(n, b)), x, c))
%o lista(nn) = forprime(p=2, nn, if (is(p), print1(p, ", "))) \\ _Michel Marcus_, Jan 24 2016
%o (Python)
%o from sympy import isprime
%o A267818_list = [int(d,4) for d in (str(i**2) for i in range(1,10**6)) if max(d) < '4' and isprime(int(d,4))] # _Chai Wah Wu_, Feb 22 2016
%Y In other bases: A267817, A267818, A267819, A267820, A267821, A241246, A267490.
%K nonn,base
%O 1,1
%A _Christopher Cormier_, Jan 20 2016
%E a(8)-a(22) from _Chai Wah Wu_, Feb 22 2016
|
