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A267818 Primes whose base-4 representation is a square when read in base 10. 1
673, 1165921, 6228961, 53378329, 128818873, 805379161, 926711449, 1542173569, 2459671993, 8365652929, 14232980953, 26484614209, 30755887321, 31937961241, 37968797689, 78180076129, 80974979329, 97835803129, 168394504129, 314911422913, 410879716321, 529074406681 (list; graph; refs; listen; history; text; internal format)
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 A124942

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

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Last modified September 23 13:52 EDT 2021. Contains 347617 sequences. (Running on oeis4.)