

A132675


Decimal number representations of hexadecimal numbers whose form spells an AmericanEnglish word found in a standard dictionary in lexicographic order.


2



10, 2746, 703178, 44013, 11325150, 181202413, 2766, 44269, 173, 2781, 712173, 2986, 47789, 47806, 2989, 47838, 47871, 12255213, 190, 48813, 12496365, 3053, 12508653, 3054, 48879, 12513261, 3243, 3245, 51934, 51966, 52958, 847341, 3310
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OFFSET

1,1


COMMENTS

Also the decimal number equivalent of common US words using any of the letters 'a' through 'f'.
D. 5. "Here's a trick question: What would 190 in hexadecimal be? This number would be written as 11*16+14, or B*16+E. The answer is BE, the last word of my question" This is an example of a self describing question.
The list of words in lexicographical order is
"a, aba, abaca, abed, accede, acceded, ace, aced, ad, add, added, baa, baad, babe, bad, bade, baff, baffed, be, bead, beaded, bed, bedded, bee, beef, beefed, cab, cad, cade, cafe, cede, ceded, cee, dab, dabbed, dace, dad, daff, dead, deaf, decade, dee, deed, deeded, deface, defaced, ebb, ebbed, efface, effaced, fa, facade, face, faced, fad, fade, faded, fed, fee, feed."
Abe and Bea are not present in the list since they are contractions of proper names as well as Abba, Dada, Ad0be and 1ce.


REFERENCES

Arthur T. Benjamin, "The Joy of Mathematics", The Great Courses Series by The Teaching Company, Course Guide Book and DVD's, Lecture 2, 'The Joy of Numbers'.
Philip Babcock Gove, EditorinChief, Webster's Third New International Dictionary of the English Language, Unabridged, G. & C. Merriam Co., Publishers, Springfield, MA, 1961.
Official Scrabble Players Dictionary, The Official Reference For Recreational And School Play, Authorized by the makers of Scrabble (R) Brand crossword games and endorsed by the National Scrabble (R) Association.
John Simpson, Chief Editor, Oxford English Dictionary, Oxford University Press, 2007.
Webster's New Collegiate Dictionary, G. & C. Merriam Co., Publishers, Springfield, MA.


LINKS

Table of n, a(n) for n=1..33.
Arthur T. Benjamin, Home page.
Scrabble, Home Page
John Simpson, The Oxford English Dictionary.
Teaching Company, The Joy of Mathematics.
Eric Weisstein's World of Mathematics, Hexadecimal.
Wikipedia, The Oxford English Dictionary.
Wikipedia, The Official Scrabble Players Dictionary.


EXAMPLE

"D. The hexadecimal system is also used frequently in computers. 1. In this system instead of having ten digits, 0 through 9, or two digits, 0 and 1, [as in the binary system] we have sixteen digits. These are the digits 0 through 9, along with A, B, C, D, E and F, which represent the numbers 10, 11, 12, 13, 14 and 15. 2. In base 10, the number 42 would be represented as four 10s and one 2, but in a hexadecimal system, 42 would be four 16s and one 2, or 4*16+2*1=66... ."


MATHEMATICA

lst = {a, aba, abaca, abed, accede, acceded, ace, aced, ad, add, added, baa, baad, babe, bad, bade, baff, baffed, be, bead, beaded, bed, bedded, bee, beef, beefed, cab, cad, cade, cafe, cede, ceded, cee, dab, dabbed, dace, dad, daff, dead, deaf, decade, dee, deed, deeded, deface, defaced, ebb, ebbed, efface, effaced, fa, facade, face, faced, fad, fade, faded, fed, fee, feed};
f[ls_] := FromDigits[ ToString@ ls, 16]; f@# & /@ lst


CROSSREFS

Cf. A057946, A132676.
Sequence in context: A047945 A327002 A246116 * A227223 A208185 A123377
Adjacent sequences: A132672 A132673 A132674 * A132676 A132677 A132678


KEYWORD

base,fini,full,nonn,word,changed


AUTHOR

Arthur T. Benjamin (benjamin(AT)math.hmc.edu), Jonathan Vos Post & Robert G. Wilson v, Aug 06 2007


STATUS

approved



