OFFSET
0,1
COMMENTS
Base 36 extrapolates the use of the letters of the alphabet as placeholders, as in the more familiar base-16's A, B, C, D, E, F, all the way to Z.
REFERENCES
M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002).
LINKS
Landon Curt Noll, The English Name of a Number
Eric Weisstein's World of Mathematics, Number
Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens .
M. J. Halm, Jootsy Calculus.
FORMULA
In base 36 A = 10, B = 11, ..., Z = 35
EXAMPLE
a(0) = 1652100 because zero (base 36) = z(36^3) + e(36^2) + r(36) + o = 35(46656) + 14(1296) + 27(36) + 24 = 1632960 + 18144 + 972 + 24 = 1652100 (base 10).
MATHEMATICA
lst = {zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, twentyone, twentytwo, twentythree, twentyfour, twentyfive, twentysix, twentyseven, twentyeight, twentynine, thirty, thirtyone, thirtytwo, thirtythree, thirtyfour, thirtyfive, thirtysix, thirtyseven, thirtyeight, thirtynine, forty, fortyone, fortytwo, fortythree, fortyfour, fortyfive, fortysix, fortyseven, fortyeight, fortynine, fifty};
f[ls_] := FromDigits[ToString@ls, 36]; f@# & /@ lst (* Robert G. Wilson v, Aug 26 2007 *)
PROG
(Python)
from num2words import num2words
def n2w(n): return "".join(c for c in num2words(n).replace(" and", "") if c.isalpha())
def a(n): return int(n2w(n), 36)
print([a(n) for n in range(23)]) # Michael S. Branicky, Jan 15 2026
CROSSREFS
KEYWORD
word,base,nonn
AUTHOR
Michael Joseph Halm, Aug 19 2002
EXTENSIONS
a(14) and a(17) corrected and more terms from Sean A. Irvine, Nov 04 2024
STATUS
approved