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Search: id:A143027
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| A143027 |
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Sturdy prime numbers: p such that in binary notation k*p has at least as many 1-bits as p for all k>0. |
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+0
3
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| 2, 3, 5, 7, 17, 31, 73, 89, 127, 257, 1801, 2089, 8191, 65537, 131071, 178481, 262657, 524287
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The primes in A125121. This sequence includes the Fermat primes (A019434), Mersenne primes (A000668) and the three known primes in A051154, It appears that almost all primes are flimsy numbers, A005360.
Ray Chandler found 2089 and 8191.
Odd sturdy primes appear to be the largest primitive prime factor of 2^q-1 for q a prime or prime power. The values of q for the current terms: 2, 4, 3, 8, 5, 9, 11, 16, 25, 29, 13, 32, 17, 23, 27 and 19. The sequence probably continues with 2099863, 6700417, 13264529, 20394401, 97685839.
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CROSSREFS
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Sequence in context: A103384 A103383 A103382 this_sequence A001153 A141453 A100532
Adjacent sequences: A143024 A143025 A143026 this_sequence A143028 A143029 A143030
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KEYWORD
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more,nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 17 2008, Jul 21 2008
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