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A073029 Names for numbers in American English, with each letter transformed into its index in the alphabet.

%I A073029 #42 Jul 28 2025 00:01:47
%S A073029 26,5,18,15,15,14,5,20,23,15,20,8,18,5,5,6,15,21,18,6,9,22,5,19,9,24,
%T A073029 19,5,22,5,14,5,9,7,8,20,14,9,14,5,20,5,14,5,12,5,22,5,14,20,23,5,12,
%U A073029 22,5,20,8,9,18,20,5,5,14,6,15,21,18,20,5,5,14,6,9,6,20,5,5,14,19,9,24,20,5
%N A073029 Names for numbers in American English, with each letter transformed into its index in the alphabet.
%C A073029 Irregular triangle read by rows, in which row n lists the successive indices of the letters in the American English name for n. For example, row one is 15, 14, 5. - _N. J. A. Sloane_, Apr 22 2023
%C A073029 Find smallest n's for which a(n)=1,2,3,4,...,26.
%C A073029 A: The numbers 10 and 11 never occur. The rows in which the others occur first (assuming use of the "short scale") are 1000 (thousAnd), 10^9 (Billion), 10^27 (oCtillion), 100 (hunDred), 0 (zEro), 4 (Four), 8 (eiGht), 3 (tHree), 5 (fIve), --, -- (j & k don't occur in English names of numbers), 11 (eLeven), 10^6 (Million), 1 (oNe), 0 (zerO), 10^24 (sePtillion), 10^15 (Quadrillion), 0 (zeRo), 6 (Six), 2 (Two), 4 (foUr), 5 (fiVe), 2 (tWo), 6 (siX), 20 (twentY), 0 (Zero). Converting the position in the row plus the preceding row lengths to a linear index n this yields (after subtracting 1 to match offset 0 of the sequence): 18452, ?, ?, 864, 1, 15, 33, 11, 20, -, -, 44, ?, 5, 3, ?, ?, 2, 23, 7, 17, 21, 8, 25, 115, 0. The graph nicely shows the position & frequency of the individual letters. - _M. F. Hasler_, Feb 06 2016
%H A073029 M. F. Hasler, <a href="/A073029/b073029.txt">Table of n, a(n) for n = 0..18454</a> (rows 0..1000 "flattened"), Feb 06 2016
%H A073029 M. F. Hasler, <a href="/A073029/a073029.txt">rows 0 - 1000</a>, Feb 06 2016
%H A073029 Robert G. Wilson v, <a href="/A001477/a001477.txt">American English names for the numbers from 0 to 100999 without spaces or hyphens</a>, Jun 08 2010
%e A073029 Top row is for "zero"; "z" is the 26th letter in the alphabet, "e" the fifth, "r" the 18th and "o" the 15th, so the first row is 26,5,18,15.
%t A073029 alef=Characters["abcdefghijklmnopqrstuvwxyz"]; numb="zeroonetwothreefourfivesixseveneightnineteneleven[...]"; ch=Characters[numb]; seq[n_] := Position[alef, ch[[n]]][[1, 1]] (* _Franklin T. Adams-Watters_, Jun 02 2006 *)
%t A073029 (* see the link to a001477.txt, copy the first 17 lines and then paste and assign to the variable 'str' as a string as follows *)
%t A073029 str = "zeroonetwothreefourfivesixseveneightnineteneleventwelvethirteenfourteenfifteensixteen";
%t A073029 Characters@ str /. Flatten[ Table[ {FromCharacterCode[96 + n] -> n}, {n, 26}]] (* _Robert G. Wilson v_, Jun 08 2010 *)
%o A073029 (PARI) A073029_row(n)=select(t->t>64,Vec(Vecsmall(English(n))))%32 \\ See A052360 for English(). - _M. F. Hasler_, Feb 06 2016
%o A073029 (Python)
%o A073029 from num2words import num2words
%o A073029 def row(n): return [ord(c)-96 for c in num2words(n).replace(" and", "") if c.isalpha()]
%o A073029 print([e for n in range(17) for e in row(n)]) # _Michael S. Branicky_, Apr 22 2023
%Y A073029 Cf. A005589 (row lengths).
%Y A073029 Cf. A073327 (row sums).
%Y A073029 Cf. A072922.
%K A073029 word,nonn,easy,tabf,look
%O A073029 0,1
%A A073029 _Zak Seidov_, Aug 22 2002
%E A073029 Corrected and extended by _Franklin T. Adams-Watters_, Jun 02 2006, Oct 24 2006