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A121863
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See Comments lines for definition.
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5
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OFFSET
| 4,1
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COMMENTS
| Let "N_b" denote "N read in base b" and let "N" denote "N written in base 10" (as in normal life). The sequence is given by 16, 32_16, 64_(32_16), 128_(64_(32_16)), etc., or in other words
......16....32.....64....128.......etc.
..............16.....32.....64.........
.......................16.....32.......
................................16.....
where the subscripts are evaluated from the bottom upwards.
More precisely, "N_b" means "Take decimal expansion of N and evaluate it as if it were a base-b expansion".
The next term is too large to include.
A "dungeon" of numbers.
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REFERENCES
| David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.
David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 393-402.
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LINKS
| David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing (arXiv:math.NT/0611293).
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EXAMPLE
| 64_(32_16) = 64_(3*16 + 2) = 64_50 = 6*50 + 4 = 304.
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PROG
| (PARI) rebase(n, bas)={ local(resul, i) ; resul= n % 10 ; i=1 ; while(n>0, n = n \10 ; resul += (n%10)*bas^i ; i++ ; ) ; return(resul) ; } { a=16 ; print(a) ; for(n=5, 12, a=2^n ; forstep(j=n, 5, -1, a=rebase(2^(j-1), a) ; ) ; print1(a, ", ") ; ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 01 2006
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CROSSREFS
| Cf. A121864, A121263, A121266, A121264, A121265, A121295, A121296, A111050, A121866, A122030.
Sequence in context: A030688 A186850 A186842 * A121864 A204723 A204962
Adjacent sequences: A121860 A121861 A121862 * A121864 A121865 A121866
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KEYWORD
| nonn,base
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 31 2006, corrected Sep 05 2006
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 01 2006
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