A171252 Least power of 2 to have at least n consecutive digits 'n' in its decimal expansion.
0, 0, 43, 83, 192, 973, 2269, 972, 25263, 42485
Offset: 0
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a(3)=157 because 2^157(i.e. 182687704666362864775460604089535377456991567872) is the smallest power of 2 to contain a run of 3 consecutive sixes in its decimal form.
a = ""; Do[ a = StringJoin[a, "6"]; b = StringJoin[a, "6"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]
a(3)=24 because 2^24(i.e. 16777216) is the smallest power of 2 to contain a run of 3 consecutive sevens in its decimal form.
a = ""; Do[ a = StringJoin[a, "7"]; b = StringJoin[a, "7"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]
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