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 A238448 Smallest number m such that 2^m contains a string of n consecutive increasing digits in its decimal representation. 3
 0, 7, 28, 135, 391, 992, 5837, 9485, 15975, 244178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is an increasing sequence (but not necessarily strictly increasing). LINKS EXAMPLE 7 is the smallest exponent such that 2^7 contains two consecutive increasing digits (2^7 = 128). 28 is the smallest exponent such that 2^28 ( = 268435456)  contains three consecutive increasing digits (456). a(6) = 992 from  2^992 = 418558049682135672245478534789063207250548754572474065407714995457168379_345\     678_17284890561672488119458109166910841919797858872862722356017328064756\     15116630782786940537040715228680107267602488727296075852403533779290461\     69580757764357779904060393635270100437362409630553424235540298930640110\     82834640896 - N. J. A. Sloane, Aug 12 2018 MATHEMATICA a[1]=0; a[n_] := Block[{k = 4, p = 16}, While[Max[ Length /@ Select[ Split@ Differences@ IntegerDigits@p, First@# == 1 &]] < n-1, k++; p *= 2]; k]; a/@ Range[7] (* Giovanni Resta, Feb 26 2014 *) PROG (Python) def Str(x): ..for n in range(10**5): ....count = 0 ....i = 0 ....if len(str(2**n)) == x and x == 1: ......return n ....while i < len(str(2**n))-1: ......if int(str(2**n)[i]) == int(str(2**n)[i+1])-1: ........count += 1 ........i += 1 ......else: ........if count == x-1: ..........return n ........else: ..........count = 0 ..........i += 1 ....if count == x-1: ......return n x = 1 while x < 50: ..print(Str(x)) ..x += 1 CROSSREFS Cf. A045875. Sequence in context: A219737 A316106 A249872 * A290356 A025030 A001554 Adjacent sequences:  A238445 A238446 A238447 * A238449 A238450 A238451 KEYWORD nonn,base,fini,full AUTHOR Derek Orr, Feb 26 2014 EXTENSIONS a(8)-a(10) from Giovanni Resta, Feb 26 2014 Definition and examples corrected ("integers" changed to "digits") by N. J. A. Sloane, Aug 12 2018 STATUS approved

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Last modified September 28 21:53 EDT 2020. Contains 337414 sequences. (Running on oeis4.)