

A131537


Least exponent k such that 2^k has exactly n consecutive 3's in its decimal representation.


2



5, 25, 83, 219, 221, 2270, 11020, 18843, 192915, 271978, 743748, 1039315, 13873203, 14060685
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OFFSET

1,1


COMMENTS

No more terms < 28*10^6.


LINKS

Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC916.


EXAMPLE

a(3) = 83 because 2^83 (= 9671406556917033397649408) is the smallest power of 2 to contain a run of exactly 3 consecutive threes in its decimal form.


MATHEMATICA

a = ""; Do[ a = StringJoin[a, "3"]; b = StringJoin[a, "3"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {}  StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 9} ]


PROG

(Python)
def a(n):
k, n2, np2 = 1, '3'*n, '3'*(n+1)
while True:
while not n2 in str(2**k): k += 1
if np2 not in str(2**k): return k
k += 1


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS



STATUS

approved



