|
Search: id:A133832
|
|
|
| A133832 |
|
Least number k>n such that the binary trinomial 1 + 2^n + 2^k is prime, or 0 if there is no such k. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..255
|
|
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}]
|
|
CROSSREFS
|
Cf. A057732, A059242, A057196, A057200, A081091, A095056 (various forms of prime binary trinomials).
Sequence in context: A000997 A107475 A108225 this_sequence A061488 A111239 A145343
Adjacent sequences: A133829 A133830 A133831 this_sequence A133833 A133834 A133835
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Sep 26 2007
|
|
|
Search completed in 0.002 seconds
|
