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A267818
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Primes whose base-4 representation is a square when read in base 10.
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1
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673, 1165921, 6228961, 53378329, 128818873, 805379161, 926711449, 1542173569, 2459671993, 8365652929, 14232980953, 26484614209, 30755887321, 31937961241, 37968797689, 78180076129, 80974979329, 97835803129, 168394504129, 314911422913, 410879716321, 529074406681
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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673 written in base 4 is 22201, and 22201 in base 10 is 149^2.
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MATHEMATICA
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Select[Prime@ Range[10^6], IntegerQ@ Sqrt@ FromDigits@ IntegerDigits[#, 4] &] (* Michael De Vlieger, Jan 24 2016 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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