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Search: id:A065047
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| A065047 |
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Primes which when written in base 2 and prepended with a 1 produce a prime. |
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+0
1
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| 3, 5, 13, 29, 37, 43, 71, 83, 101, 113, 163, 193, 211, 223, 257, 311, 317, 347, 479, 509, 547, 577, 613, 643, 673, 709, 787, 823, 853, 877, 883, 907, 1031, 1061, 1181, 1223, 1259, 1283, 1409, 1451, 1481, 1493, 1499, 1511, 1523, 1559, 1583, 1721, 1871, 1973
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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EXAMPLE
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13 is in the sequence because 13d = 1101b, prepend a one gives 11101b = 29d which is a prime.
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MATHEMATICA
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Do[p = Prime[n]; d = IntegerDigits[p, 2]; If[ PrimeQ[ FromDigits[ Prepend[d, 1], 2]], Print[p]], {n, 1, 350} ]
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PROGRAM
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(PARI) { n=0; t=log(2); for (m=1, 10^9, p=prime(m); if (isprime(p + 2^(1 + log(p)\t)), write("b065047.txt", n++, " ", p); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 05 2009]
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CROSSREFS
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Cf. A059459.
Sequence in context: A077443 A147196 A110225 this_sequence A067932 A106666 A124791
Adjacent sequences: A065044 A065045 A065046 this_sequence A065048 A065049 A065050
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KEYWORD
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base,easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 05 2001
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