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 A256590 Base-2 Reacher numbers: numbers n that are powers of the sum of their base-2 digits. 1
 0, 1, 81, 625, 7776, 16807, 46656, 59049, 1679616, 1475789056, 6975757441, 137858491849, 576650390625, 41426511213649, 2384185791015625, 150094635296999121, 10260628712958602189, 32768000000000000000, 243569224216081305397, 655360000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Named for fictional character Jack Reacher in the series of novels by Lee Child. There are 2709 terms with 10,000 or fewer digits; a(2709) = 15402^2388. - Charles R Greathouse IV, Nov 26 2016 REFERENCES Lee Child, Bad Luck and Trouble, Delacorte Press, 2007.  In this book, the main character, Jack Reacher, likes the number 81 because it is the square of the sum of its base-10 digits. LINKS Hiroaki Yamanouchi and Charles R Greathouse IV, Table of n, a(n) for n = 1..388 (first 141 terms from Hiroaki Yamanouchi) J. Shallit, Mathematics in a Jack Reacher Novel, blog post, Sep 08 2007. MATHEMATICA fQ[n_] := Block[{wt = DigitCount[n, 2, 1]}, Which[n <= 1, True, wt <= 1, False, True, IntegerQ@ Log[wt, n]]]; Select[Range[10^5], fQ] (* Michael De Vlieger, Apr 04 2015 *) PROG (PARI) is(n)= n<=1 || (ispower(n, , &r) && (r==hammingweight(n) || (r^ispower(n=hammingweight(n))==n && n>1))) \\ Michel Marcus and M. F. Hasler, Apr 04 2015 (PARI) list(lim)=my(v=List([0, 1]), H, t); for(e=3, logint(lim\=1, 3), for(b=2, min(solve(x=e, lim, x-e*log(x)/log(2)-1), sqrtnint(lim, e)), H=hammingweight(t=b^e); if(H>1 && b^valuation(H, b)==H, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Nov 26 2016 CROSSREFS Cf. A023106. Sequence in context: A206064 A016756 A182647 * A185856 A185848 A237629 Adjacent sequences:  A256587 A256588 A256589 * A256591 A256592 A256593 KEYWORD nonn,base AUTHOR Jeffrey Shallit, Apr 03 2015 EXTENSIONS a(1) prepended and a(14)-a(20) added by Hiroaki Yamanouchi, Apr 03 2015 STATUS approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.