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A133832
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Least 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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1
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2, 3, 5, 13, 6, 7, 9, 9, 18, 19, 14, 13, 15, 17, 17, 81, 20, 19, 30, 33, 26, 27, 38, 81, 27, 35, 31, 33, 35, 31, 42, 458465, 36, 45, 47, 37, 67, 53, 41, 57, 42, 45, 46, 69, 54, 57, 53, 1009, 100, 119, 55, 73, 83, 67, 57, 1265, 74, 69, 66, 113, 75, 101, 66, 2241, 68, 67, 70
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: a(n) exists 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). The conjecture is equivalent to no Sierpinski numbers of the form 2^m+1 existing. The PFGW program was used to find a(32), which produces a 138012-digit probable prime.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..255
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MATHEMATICA
| mx=4000; Table[s=1+2^n; k=n+1; While[k<mx && !PrimeQ[s+2^k], k++ ]; If[k==mx, 0, k], {n, 100}]
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CROSSREFS
| Cf. A057732, A059242, A057196, A057200, A081091, A095056 (various forms of prime binary trinomials).
Sequence in context: A107475 A108225 A193064 * A061488 A111239 A145343
Adjacent sequences: A133829 A133830 A133831 * A133833 A133834 A133835
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 26 2007
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