cp's OEIS Frontend

A132676 Decimal number representations of hexadecimal numbers whose form spells an American-English word found in a standard dictionary in numerical order.

%I A132676 #12 Feb 16 2025 08:33:06
%S A132676 10,173,190,250,2746,2766,2781,2986,2989,3053,3054,3243,3245,3310,
%T A132676 3499,3501,3566,3771,4013,4077,4078,44013,44269,47789,47806,47838,
%U A132676 47871,48813,48879,51934,51966,52958,56014,56063,57005,57007,57069,64206
%N A132676 Decimal number representations of hexadecimal numbers whose form spells an American-English word found in a standard dictionary in numerical order.
%C A132676 Also the decimal number equivalent of common US words using any of the letters 'a' through 'f'.
%C A132676 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.
%C A132676 The list of words in lexicographical order is
%C A132676 "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."
%C A132676 Abe and Bea are not present in the list since they are contractions of proper names as well as Abba, Dada, Ad0be and 1ce.
%D A132676 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'.
%D A132676 Philip Babcock Gove, Editor, Webster's Third New International Dictionary of the English Language, Unabridged, G. & C. Merriam Co., Publishers, Springfield, MA, 1961.
%D A132676 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.
%D A132676 John Simpson, Editor, Oxford English Dictionary, Oxford University Press, 2007.
%D A132676 Webster's New Collegiate Dictionary, G. & C. Merriam Co., Publishers, Springfield, MA.
%H A132676 Arthur T. Benjamin, <a href="http://www.math.hmc.edu/~benjamin/">Home page</a>.
%H A132676 Scrabble, <a href="http://www.scrabble.com/">Home Page</a>
%H A132676 John Simpson, <a href="http://www.oed.com/">The Oxford English Dictionary</a>.
%H A132676 Teaching Company, <a href="http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1411&amp;id=1411&amp;pc=Science%20and%20Mathematics">The Joy of Mathematics</a>.
%H A132676 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>.
%H A132676 Wikipedia, <a href="http://en.wikipedia.org/wiki/Oxford_English_Dictionary">The Oxford English Dictionary</a>.
%H A132676 Wikipedia, <a href="http://en.wikipedia.org/wiki/Official_Scrabble_Players_Dictionary">The Official Scrabble Players Dictionary</a>.
%e A132676 "D. The hexadecimal system is also used frequently in
%e A132676 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... ."
%t A132676 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};
%t A132676 f[ls_] := FromDigits[ ToString@ ls, 16]; Sort[f@# & /@ lst]
%Y A132676 Cf. A057946, A132675.
%K A132676 base,fini,full,nonn,word
%O A132676 1,1
%A A132676 Arthur T. Benjamin (benjamin(AT)math.hmc.edu), _Jonathan Vos Post_ & _Robert G. Wilson v_, Aug 06 2007