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A065049
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Odd primes of incorrect parity: number of 1's in the binary representation of n (mod 2) == 1 - (n mod 3) (mod 2). Also called isolated primes.
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5
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11, 41, 43, 47, 59, 107, 131, 137, 139, 163, 167, 173, 179, 191, 227, 233, 239, 251, 277, 337, 349, 373, 419, 431, 443, 491, 521, 523, 547, 557, 563, 569, 571, 587, 617, 619, 641, 643, 647, 653, 659, 673, 677, 691, 701, 719, 739, 743, 751, 761, 809, 811
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OFFSET
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1,1
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COMMENTS
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"The prime maze - consider the prime numbers in base 2, starting with the smalles prime (10)2. One can move to another prime number by either changing only one digit of the number, or adding a 1 to the front of the number. Can we reach 11 = (1011)2.? 333? The Mersennes?" - Caldwell
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LINKS
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Table of n, a(n) for n=1..52.
Chris K. Caldwell (caldwell(AT)utm.edu), Prime Links + +
W. Paulsen, The Prime Maze, Fib. Quart., 40 (2002), 272-279.
C. Rivera, Problem 25 - William Paulsen's Prime Numbers Maze
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EXAMPLE
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47 is in the sequence because 47d = 101111b which has five 1's in its binary notation; an odd number. Also 47 == 2 (mod 3); an even number. Therefore a mismatch exists.
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MATHEMATICA
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Select[ Range[3, 1000, 2], PrimeQ[ # ] && EvenQ[ Count[ IntegerDigits[ #, 2], 1]] == OddQ[ Mod[ #, 3]] & ]
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CROSSREFS
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Sequence in context: A088622 A121171 A065079 * A158201 A122015 A192820
Adjacent sequences: A065046 A065047 A065048 * A065050 A065051 A065052
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KEYWORD
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easy,nonn
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AUTHOR
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Robert G. Wilson v, Nov 06 2001
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STATUS
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approved
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