A038842 -id:A038842 - cp's OEIS frontend

A072922 Spell English name for n, then interpret as number in base 36.

1652100, 31946, 38760, 49537526, 732051, 724298, 36969, 47723135, 24375809, 1097258, 38111, 882492287, 1807948346, 2310701170991, 1229565944111, 33766692143, 62095095599, 80156542487855, 1137277763375, 1842973464623, 1807950886, 84351756569162, 84351756575976

Offset: 0

Michael Joseph Halm, Aug 19 2002

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.

			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).

M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002).

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.

Cf. A038842.

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 *)

In base 36 A = 10, B = 11, ..., Z = 35

a(14) and a(17) corrected and more terms from Sean A. Irvine, Nov 04 2024

A182380 Primes whose base 26 representation (using a=1, b=2, ..., y=25, z=0) form English words or phrases.

Original entry on oeis.org

31, 53, 61, 67, 109, 149, 157, 197, 223, 313, 347, 353, 359, 379, 409, 421, 503, 509, 521, 613, 691, 743, 859, 863, 929, 1049, 1097, 1163, 1181, 1201, 1249, 1487, 1489, 1601, 2281, 2437, 2441, 2521, 2579, 2741, 2753

Offset: 1

Patrick Devlin, Apr 27 2012

Some particularly pleasing prime words and phrases are (with capitals added merely for visual clarity): [discovered by Patrick Devlin, April 2012]
   "somePrime" -> 4092274325963
   "somePrimeWordSequence" -> 390521469300124399570501784387
   "thisIsAGoodExampleOfAPrimePhrase"
     -> 1486423446502142057087542429696717235339605927
  And some OEIS-themed prime (pseudo-)words and phrases are:
   "NJAS" -> 252869
   "integers" -> 76851151747
   "welcomeToOEIS" -> 2214931257921335609
   "theOEISWordPrime" -> 34075123572372820632427
Let w be any phrase (e.g., w could be Homer's Iliad, or w could be the unabridged concatenation of all of Shakespeare's works). Then Dirichlet's theorem on arithmetic progressions implies that if the last letter of w is relatively prime to 26, then there are infinitely many primes whose final digits base 26 are exactly w.  There is no guarantee, however, that these primes would be prime phrases since there is essentially no control over how the beginnings of these base 26 representations would look.

			The English word "beg" becomes 2*26^2 + 5*26 + 7 = 1489, which is prime, so 1489 is in the sequence.  Similarly, "bee" becomes 1487, which is also prime (thus, "bee" and "beg" are the first 'twin prime words' in this sequence).

C. K. Caldwell, The Prime Lexicon (This is for the related base 36 interpretation as in A038842)

Cf. A038842 (base 36 version), A072922.

# To test if a word  w="someword" [all lowercase]  corresponds to a prime,
# call isprime(wordToNumber(w))  or  ifactor(wordToNumber(w))
letters:=["a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z"]:
wordToNumber:=proc(w) local lastLetter, i:
    if length(w) = 0 then return 0: end if:
    lastLetter := w[length(w)]:
    for i to nops(letters) - 1 do if letters[i] = lastLetter then return i + 26*wordToNumber(w[1 .. length(w) - 1]): fi: od:
    return 26*wordToNumber(w[1 .. length(w) - 1]):
end proc:

cp's OEIS Frontend

A072922 Spell English name for n, then interpret as number in base 36.

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