A090587 Smallest prime with exactly n consecutive zeros in the longest run of zeros in its binary expansion.

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

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 A154262

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