A267818 Primes whose base-4 representation is a square when read in base 10.

673, 1165921, 6228961, 53378329, 128818873, 805379161, 926711449, 1542173569, 2459671993, 8365652929, 14232980953, 26484614209, 30755887321, 31937961241, 37968797689, 78180076129, 80974979329, 97835803129, 168394504129, 314911422913, 410879716321, 529074406681

Offset

1,1

Comments

Primes in the sequence A267764.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..100

Example

673 written in base 4 is 22201, and 22201 in base 10 is 149^2.

Mathematica

Select[Prime@ Range[10^6], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 4] &] (* Michael De Vlieger, Jan 24 2016 *)

Prog

(PARI) is(n, b=4, c=10)=issquare(subst(Pol(digits(n, b)), x, c))
lista(nn) = forprime(p=2, nn, if (is(p), print1(p, ", "))) \\ Michel Marcus, Jan 24 2016
(Python)
from sympy import isprime
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

Crossrefs

In other bases: A267817, A267818, A267819, A267820, A267821, A241246, A267490.

Sequence in context: A160209 A234117 A171266 * A158392 A264328 A379164

Adjacent sequences: A267815 A267816 A267817 * A267819 A267820 A267821

Keyword

nonn,base

Author

Christopher Cormier, Jan 20 2016

Extensions

a(8)-a(22) from Chai Wah Wu, Feb 22 2016

Status

approved