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 A175924 Smallest power of 2 with n repeated digits. 0
 1, 65536, 16777216, 2199023255552, 1684996666696914987166688442938726917102321526408785780068975640576 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The subsequent terms are too large to display. a(6) and a(7), 2^971 and 2^972, respectively, both of which have 293 digits; a(8), 2^8554, has 2576 digits. a(9), 2^42485, has 12790 digits. Corresponding exponents of 2 are 0, 16, 24, 41, 220, 971, 972, 8554, 42485, 42486, 271979. [Zak Seidov, Oct 19 2010] LINKS Wikipedia, Power of 2 EXAMPLE a(1) is 1 because it is the first power of 2; all integers have at least one digit. a(2) is 65536 because it is the first power of 2 with two of the same digit in a row. a(3) is 16777216 because it is the first power of 2 with three of the same digit in a row. MATHEMATICA f[n_] := Block[{k = 0}, While[ !MemberQ[Length /@ Split@ IntegerDigits[2^k], n], k++ ]; 2^k]; Table[f[n], {n, 5}] (* Robert G. Wilson v, Oct 21 2010 *) PROG (Python) import math for N in xrange(1, 10): .repdigits = 1 .n = 0 .while repdigits < N: ..n += 1 ..s = str(2 ** n) ..prev = "" ..repdigits = maxrepdigits = 1 ..for d in s: ...if d == prev: repdigits += 1 ...else: ....maxrepdigits = max(maxrepdigits, repdigits) ....repdigits = 1 ...prev = d ..repdigits = max(maxrepdigits, repdigits) .print N, 2 ** n CROSSREFS Subsequence of A000079 (powers of 2). Cf. A045875. Sequence in context: A242323 A016784 A016808 * A016904 A017696 A211199 Adjacent sequences:  A175921 A175922 A175923 * A175925 A175926 A175927 KEYWORD base,nonn AUTHOR Grant Garcia, Oct 18 2010, Oct 20 2010 STATUS approved

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)