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Search: id:A133122
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| A133122 |
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Odd numbers which cannot be written as the sum of an odd prime and 2^i with i>0. |
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+0
2
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| 3, 127, 149, 251, 331, 337, 373, 509, 599, 701, 757, 809, 877, 905, 907, 959, 977, 997, 1019, 1087, 1199, 1207, 1211, 1243, 1259, 1271, 1477, 1529, 1541, 1549, 1589, 1597, 1619, 1649, 1657, 1719, 1759, 1777, 1783, 1807, 1829, 1859, 1867, 1927, 1969, 1973
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence of "obstinate numbers", that is, odd numbers which cannot be written as prime + 2^i with i >= 0 is the same except for the initial 3. - njas, Apr 20 2008
The reference by Nathanson gives on page 206 a theorem of Erdos: There exists an infinite arithmetic progression of odd positive integers, none of which is of the form p+2^k.
Essentially the same as A006285. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2008
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REFERENCES
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Nathanson, Melvyn B.; Additive Number Theory: The Classical Bases; Springer 1996
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 62.
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EXAMPLE
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a(2)=127 because none of the numbers 127-2, 127-4, 127-8, 127-16, 127-32, 127-64 is a prime.
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MAPLE
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(Maple program which returns -1 iff 2n+1 is obstinate, from njas, Apr 20 2008): f:=proc(n) local i, t1; t1:=2*n+1; i:=0; while 2^i < t1 do if isprime(t1-2^i) then RETURN(1); fi; i:=i+1; end do; RETURN(-1); end proc;
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MATHEMATICA
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s = {}; Do[Do[s = Union[s, {Prime[n] + 2^i}], {n, 2, 200}], {i, 1, 10}]; Print[Complement[Range[3, 1000, 2], s]]
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CROSSREFS
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Sequence in context: A130614 A114877 A086154 this_sequence A139936 A142007 A071151
Adjacent sequences: A133119 A133120 A133121 this_sequence A133123 A133124 A133125
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KEYWORD
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nonn
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AUTHOR
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David Newman (davidsnewman(AT)gmail.com), Sep 18 2007
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EXTENSIONS
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More terms and corrected definition from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Sep 24 2007
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