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Search: id:A065092
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| A065092 |
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Primes with property that when written in base two complementing any single bit yields a composite number. |
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+0
2
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| 127, 173, 191, 233, 239, 251, 277, 337, 349, 373, 431, 443, 491, 557, 653, 683, 701, 733, 761, 1019, 1193, 1201, 1381, 1453, 1553, 1597, 1709, 1753, 1759, 1777, 2027, 2063, 2333, 2371, 2447, 2633, 2879, 2999, 3083, 3181, 3209, 3313, 3593, 3643, 3767
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also known as singularly dead end primes.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
William Paulsen, Are some rooms totally isolated?
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EXAMPLE
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127 is in the sequence because 127d becomes 1111111b. "Changing a 1 to a 0 [from right to left] yields rooms 126, 125, 123, 119, 111, 95, or 62, all of which are composite. Furthermore, adding a digit 1 to the left of this number produces, 255 = 11111111b which is also composite. However, this room is not completely isolated from the maze because one can drop in from room 383d = 101111111b." Paulsen.
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MATHEMATICA
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Do[d = Prepend[ IntegerDigits[ Prime[n], 2], 0]; l = Length[d]; k = 1; While[k < l && !PrimeQ[ FromDigits[ If[d[[k]] == 1, ReplacePart[d, 0, k], ReplacePart[d, 1, k]], 2]], k++ ]; If[k == l, Print[ Prime[n]]], {n, 2, 500} ]
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CROSSREFS
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Adjacent sequences: A065089 A065090 A065091 this_sequence A065093 A065094 A065095
Sequence in context: A006285 A094933 A137985 this_sequence A141916 A023689 A095284
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KEYWORD
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base,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 10 2001
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