cp's OEIS Frontend

A132675 Decimal number representations of hexadecimal numbers whose form spells an American-English word found in a standard dictionary in lexicographic order.

%I A132675 #14 Feb 16 2025 08:33:06
%S A132675 10,2746,703178,44013,11325150,181202413,2766,44269,173,2781,712173,
%T A132675 2986,47789,47806,2989,47838,47871,12255213,190,48813,12496365,3053,
%U A132675 12508653,3054,48879,12513261,3243,3245,51934,51966,52958,847341,3310
%N A132675 Decimal number representations of hexadecimal numbers whose form spells an American-English word found in a standard dictionary in lexicographic order.
%C A132675 Also the decimal number equivalent of common US words using any of the letters 'a' through 'f'.
%C A132675 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 A132675 The list of words in lexicographical order is
%C A132675 "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 A132675 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 A132675 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 A132675 Philip Babcock Gove, Editor-in-Chief, Webster's Third New International Dictionary of the English Language, Unabridged, G. & C. Merriam Co., Publishers, Springfield, MA, 1961.
%D A132675 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 A132675 John Simpson, Chief Editor, Oxford English Dictionary, Oxford University Press, 2007.
%D A132675 Webster's New Collegiate Dictionary, G. & C. Merriam Co., Publishers, Springfield, MA.
%H A132675 Arthur T. Benjamin, <a href="http://www.math.hmc.edu/~benjamin/">Home page</a>.
%H A132675 Scrabble, <a href="http://www.scrabble.com/">Home Page</a>
%H A132675 John Simpson, <a href="http://www.oed.com/">The Oxford English Dictionary</a>.
%H A132675 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 A132675 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>.
%H A132675 Wikipedia, <a href="http://en.wikipedia.org/wiki/Oxford_English_Dictionary">The Oxford English Dictionary</a>.
%H A132675 Wikipedia, <a href="http://en.wikipedia.org/wiki/Official_Scrabble_Players_Dictionary">The Official Scrabble Players Dictionary</a>.
%e A132675 "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... ."
%t A132675 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 A132675 f[ls_] := FromDigits[ ToString@ ls, 16]; f@# & /@ lst
%Y A132675 Cf. A057946, A132676.
%K A132675 base,fini,full,nonn,word
%O A132675 1,1
%A A132675 Arthur T. Benjamin (benjamin(AT)math.hmc.edu), _Jonathan Vos Post_ & _Robert G. Wilson v_, Aug 06 2007