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Search: id:A133831
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| A133831 |
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Least positive number k != n such that the binary trinomial 1 + 2^n + 2^k is prime, or 0 if there is no such k. |
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2
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| 2, 1, 1, 1, 2, 1, 1, 9, 3, 3, 2, 1, 4, 5, 1, 1, 11, 1, 6, 5, 4, 7, 3, 9, 27, 17, 15, 1, 15, 1, 6, 458465, 4, 9, 14, 13, 3, 11, 25, 57, 6, 7, 46, 17, 7, 15, 2, 1009, 30, 23, 6, 21, 2, 33, 1, 1265, 3, 69, 14, 5, 6, 21, 19, 2241, 30, 3, 1, 5, 34, 19, 26, 17, 19, 17, 5, 33, 15, 23, 27
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Does a(n) exist for all n? These binary trinomials can also be written as f*2^n+1, where f=2^m+1 for some m, which is reminiscent of the Sierpinski problem (see A076336). Hence if there are no Sierpinski numbers of the form 2^m+1, then a(n) exists for all n . The PFGW program was used to find a(32), which produces a 138012-digit probable prime. If a(256) exists, it is greater than 10^6.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..255
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MATHEMATICA
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mx=4000; Table[s=1+2^n; k=1; While[k==n || (k<mx && !PrimeQ[s+2^k]), k++ ]; If[k==mx, 0, k], {n, 100}]
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CROSSREFS
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Cf. A057732, A059242, A057196, A057200, A081091, A095056 (various forms of prime binary trinomials).
Sequence in context: A107435 A118107 A055652 this_sequence A066955 A089048 A133162
Adjacent sequences: A133828 A133829 A133830 this_sequence A133832 A133833 A133834
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 26 2007
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