A267820 Primes whose base-6 representation is a square when read in base 10.

17, 89, 409, 449, 577, 953, 7649, 12401, 14593, 23689, 28393, 29033, 30689, 36809, 40153, 46457, 47969, 54577, 56393, 59273, 65033, 72649, 78713, 92033, 98953, 106033, 141353, 146249, 150209, 169657, 176489, 199889, 205433, 221849, 235273, 238481, 245033, 258569, 381841, 394633, 441193, 529273

Offset: 1

Author

Christopher Cormier, Jan 20 2016

Keywords

• nonn
• base

Comments

Primes in the sequence A267766.

Examples

			17 in base 6 is 25, and 25 = 5^2 in base 10.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

In other bases: A267817 - A267821, A241246, A267490.

Programs

Mathematica

Select[Prime@ Range@ 45000, IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 6] &] (* Michael De Vlieger, Jan 24 2016 *)

Python

from sympy import isprime
A267820_list = [int(d,6) for d in (str(i**2) for i in range(1,10**6)) if max(d) < '6' and isprime(int(d,6))] # Chai Wah Wu, Feb 22 2016