A090593 Smallest prime with exactly n consecutive ones in the longest run of ones in its binary expansion.
2, 3, 7, 47, 31, 191, 127, 1021, 3583, 4093, 6143, 16381, 8191, 81919, 262139, 1114111, 131071, 786431, 524287, 4194301, 14680063, 16777213, 67108859, 654311423, 671088637, 738197503, 536870909, 5368709117, 3758096383, 34359738337, 2147483647, 21474836479
Offset: 1
Examples
a(1) = 2 since 2_d = 10_b. a(2) = 3 since 3_d = 11_b. a(3) = 7 since 7_d = 111_b. a(4) = 47 since 47_d = 101111_b.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..3310
Programs
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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]], 0, 2]][[ -1]]]; If[ a[[m]] == 0, a[[m]] = p]; p = NextPrim[p], {n, 1, 117000000}]
Extensions
a(28)-a(32) from Donovan Johnson, Sep 10 2013