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A131535
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Exponent of least power of 2 having exactly n consecutive 1's in its decimal representation.
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10
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1, 0, 40, 42, 313, 485, 1841, 8923, 8554, 81783, 165742, 1371683, 1727601, 9386566, 28190643, 63416789
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OFFSET
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0,3
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LINKS
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Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.
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EXAMPLE
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a(3)=42 because 2^42(i.e. 4398046511104) is the smallest power of 2 to contain a run of 3 consecutive ones in its decimal form.
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MATHEMATICA
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a = ""; Do[ a = StringJoin[a, "1"]; b = StringJoin[a, "1"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]
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PROG
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(Python)
s, t, m, k, u = '1'*n, '1'*(n+1), 0, 1, '1'
while s not in u or t in u:
m += 1
k *= 2
u = str(k)
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CROSSREFS
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KEYWORD
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more,nonn,base
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AUTHOR
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EXTENSIONS
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a(0) added and a(1) corrected by Chai Wah Wu, Jan 28 2020
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STATUS
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approved
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