login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132676 Decimal number representations of hexadecimal numbers whose form spells an American-English word found in a standard dictionary in numerical order. 2
10, 173, 190, 250, 2746, 2766, 2781, 2986, 2989, 3053, 3054, 3243, 3245, 3310, 3499, 3501, 3566, 3771, 4013, 4077, 4078, 44013, 44269, 47789, 47806, 47838, 47871, 48813, 48879, 51934, 51966, 52958, 56014, 56063, 57005, 57007, 57069, 64206 (list; graph; refs; listen; history; text; internal format)
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, Editor, 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, 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..38.

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]; Sort[f@# & /@ lst]

CROSSREFS

Cf. A057946, A132675.

Sequence in context: A133273 A239763 A112703 * A270958 A200574 A078516

Adjacent sequences:  A132673 A132674 A132675 * A132677 A132678 A132679

KEYWORD

base,fini,full,nonn,word

AUTHOR

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 17 11:14 EDT 2019. Contains 326057 sequences. (Running on oeis4.)