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A235144
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Primes whose base-10 representation also represents a prime in base 19.
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2
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2, 3, 5, 7, 23, 29, 43, 47, 113, 131, 151, 157, 179, 199, 229, 263, 283, 311, 317, 353, 359, 409, 421, 443, 461, 557, 593, 641, 661, 739, 773, 809, 821, 881, 937, 953, 977, 1031, 1109, 1213, 1217, 1231, 1279, 1291, 1297, 1307, 1433, 1439, 1583, 1657, 1693, 1697, 1741, 1789, 1811, 1873, 1877, 1949, 1987, 2003
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OFFSET
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1,1
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COMMENTS
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See A090714 for a similar sequence whose definition works "in the opposite direction".
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LINKS
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EXAMPLE
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The decimal representation of prime 23, considered as a number written in base 19, stands for 2*19 + 3 = 41, which is also prime, therefore 23 is in the sequence.
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MATHEMATICA
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Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#], 19]] &] (* Alonso del Arte, Jan 04 2014 *)
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PROG
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(PARI) is_A235144(p, b=19)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows one to produce similar sequences for other bases b > 9 (which can be given as optional 2nd argument), but does not do the required check for bases b < 10.
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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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STATUS
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approved
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