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
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