

A090587


Smallest prime with exactly n consecutive zeros in the longest run of zeros in its binary expansion.


2



3, 2, 19, 17, 67, 131, 641, 257, 2053, 10243, 4099, 12289, 40961, 32771, 65539, 65537, 262147, 786433, 4194319, 7340033, 23068673, 50331653, 67108879, 436207619, 167772161, 268435463, 268435459, 1073741831, 1073741827, 3221225473, 21474836483, 68719476767
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OFFSET

0,1


COMMENTS

Except for 2, the first and last binary digits of a prime number are 1.
One may also define a sequence of the smallest prime with its longest run of zeros containing *at least* n zeros in the binary expansion: 2, 2, 17, 17, 67, 131, 257, 257, 2053, 4099,....  R. J. Mathar, Sep 09 2013


LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..3313


FORMULA

min{ A000040(k): A090046(k) = n}.  R. J. Mathar, Sep 09 2013


EXAMPLE

a(0) = 3 since 3_d = 11_b. a(1) = 2 since 2_d = 10_b. a(3) = 17 since 17_d = 10001_b. a(6) = 641 since 641_d = 1010000001_b.


MATHEMATICA

a = Table[0, {30}]; NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; p = 2; Do[ m = Length[ Union[ DeleteCases[ Split[ IntegerDigits[p, 2]], 1, 2]][[ 1]]]; If[ a[[m + 1]] == 0, a[[m + 1]] = p]; p = NextPrim[p], {n, 1, 117000000}]


CROSSREFS

Cf. A090046, A090593.
Sequence in context: A057026 A032448 A066195 * A094554 A223881 A206582
Adjacent sequences: A090584 A090585 A090586 * A090588 A090589 A090590


KEYWORD

nonn,base


AUTHOR

Robert G. Wilson v, Dec 03 2003


EXTENSIONS

a(29)a(31) from Donovan Johnson, Sep 10 2013


STATUS

approved



