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Search: id:A091938
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| A091938 |
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Smallest prime between 2^n and 2^(n+1), having a maximal number of 1's in binary representation. |
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+0
5
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| 3, 7, 11, 31, 47, 127, 191, 383, 991, 2039, 3583, 8191, 15359, 20479, 63487, 131071, 245759, 524287, 786431, 1966079, 4128767, 7323647, 14680063, 33546239, 67108351, 100646911, 260046847, 536739839, 1073479679, 2147483647
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A091937(n) = A000120(a(n)).
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MATHEMATICA
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 2; Do[c = 0; While[p < 2^n, b = Count[ IntegerDigits[p, 2], 1]; If[c < b, c = b; q = p]; p = NextPrim[p]]; Print[q], {n, 1, 30}] (from Robert G. Wilson v Feb 21 2004)
b[n_] := Min[ Select[ FromDigits[ #, 2] & /@ (Join[{1}, #, {1}] & /@ Permutations[ Join[{0}, Table[1, {n - 2}]]]), PrimeQ[ # ] &]]; c[n_] := Min[ Select[ FromDigits[ #, 2] & /@ (Join[{1}, #, {1}] & /@ Permutations[ Join[{0, 0}, Table[1, {n - 3}]]]), PrimeQ[ # ] &]]; f[n_] := If[ PrimeQ[2^(n + 1) - 1], 2^(n + 1) - 1, If[ PrimeQ[ b[n]], b[n], c[n]]]; Table[ f[n], {n, 30}] (Robert G. Wilson v)
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CROSSREFS
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Cf. A091936, A000668.
Sequence in context: A125879 A152084 A131588 this_sequence A051919 A119175 A038913
Adjacent sequences: A091935 A091936 A091937 this_sequence A091939 A091940 A091941
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 14 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 20 2004
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