Eric Angelini Eric.Angelini@kntv.be via list.seqfan.eu Thu, Dec 5, 2013, 5:38 AM to Sequence Hello SeqFans, - this is a sequence S based on English number-names; - the sequence S is the first column on the left; - the second column is the quantity of capital letters used so far to spell the terms of the sequence; - S is always extended with the smallest English number-name that produces a smaller term on the second column than the one on its left. S Cumulative sum of letters used so far | | 5 4 FIVE 9 8 NINE 16 15 SIXTEEN 26 24 TWENTY-SIX 35 34 THIRTY-FIVE 40 39 FORTY 49 48 FORTY-NINE 59 57 FIFTY-NINE 68 67 SIXTY-EIGHT 79 78 SEVENTY-NINE 89 88 EIGHTY-NINE 99 98 NINETY-NINE 116 115 ONE HUNDRED SIXTEEN 136 134 ONE HUNDRED THIRTY-SIX 150 149 ONE HUNDRED FIFTY 169 168 ONE HUNDRED SIXTY-NINE 189 188 ONE HUNDRED EIGHTY-NINE 200 198 TWO HUNDRED 218 216 TWO HUNDRED EIGHTEEN ... - We see that we cannot start S with ONE as "ONE" has 3 letters, which is not smaller than "1"; - We cannot start S with TWO as "TWO" has 3 letters which is not smaller than "2"; - We cannot start S with THREE either because "THREE" has 5 letters which is not smaller than "3"; - We still cannot start S with FOUR because "FOUR" has 4 letters which is not strictly smaller than "4"; - But FIVE is ok because "FIVE" has 4 letters which is smaller than "5"; - We cannot extend S with "SIX" as the cumulative quantity of written letters so far would be 7, which is not smaller than "6"; - We cannot extend S with "SEVEN" as the cumulative quantity of written letters so far would be 9, which is not smaller than "7"; - We cannot extend S with "EIGHT" as the cumulative quantity of written letters so far would be 9, which is not smaller than "8"; - But "NINE" is ok because the cumulative quantity of written letters so far (NINE included) is 8, which is smaller than "9"; - If we try now to extend S with TEN, ELEVEN, TWELVE, THIRTEEN or FOURTEEN we will always exceed 10, 11, 12, 13 or 14 letters used so far (which is not allowed). If we try to extend S with FIFTEEN we will see that "FIVE NINE FIFTEEN" uses 15 letters which is forbidden too. But SIXTEEN is ok because "FIVE NINE SIXTEEN" uses 15 letters, which is less than "16". Etc. I hope this is of interest for the OEIS and does not contain too many typos. Best, É. --- Hans Havermann gladhobo@teksavvy.com via list.seqfan.eu Dec 5, 2013, 8:42 AM to Sequence > S Cumulative sum of letters used so far > | | > 5 4 FIVE > 9 8 NINE > 16 15 SIXTEEN > 26 24 TWENTY-SIX > 35 34 THIRTY-FIVE > 40 39 FORTY > 49 48 FORTY-NINE > 59 57 FIFTY-NINE > 68 67 SIXTY-EIGHT ... *66 65 SIXTY-SIX* <- last line should be, then: 76 75 seventy-six 86 84 eighty-six 95 94 ninety-five 109 108 one hundred nine 129 128 one hundred twenty-nine 149 147 one hundred forty-nine 166 165 one hundred sixty-six 186 184 one hundred eighty-six 200 194 two hundred 209 208 two hundred nine 229 228 two hundred twenty-nine --- Eric Angelini Eric.Angelini@kntv.be via list.seqfan.eu Thu, Dec 5, 2013, 8:59 AM to Sequence Aaaaaarghhh... well spotted, Hans... Back to the blackboard :-(( Best, É. --- Ron Hardin rhhardin@att.net via list.seqfan.eu Dec 5, 2013, 9:13 AM to Sequence Slightly related is Hoey's inequality The (English) length of number n's name is less than or equal to .3n+4.1 which is at the bottom of http://selfreferentialsentences.blogspot.com/ by proving it exhaustive. rhhardin@mindspring.com rhhardin@att.net (either) -- M. F. Hasler oeis@hasler.fr via list.seqfan.eu Thu, Dec 5, 2013, 9:23 AM to Sequence On Thu, Dec 5, 2013 at 6:35 AM, Eric Angelini wrote: > - this is a sequence S based on English number-names; > - the sequence S is the first column on the left; > - the second column is the quantity of capital > letters used so far to spell the terms of the > sequence; > - S is always extended with the smallest English > number-name that produces a smaller term on the > second column than the one on its left. proposed as https://oeis.org/draft/A233184 It seems that using "not larger" instead of "smaller" would only change the first term from 5 to 4. Maximilian -- Eric Angelini Eric.Angelini@kntv.be via list.seqfan.eu Thu, Dec 5, 2013, 9:27 AM to Sequence > It seems that using "not larger" instead of "smaller" would only change the first term from 5 to 4. ... yes, indeed -- well done, Maximilian, and thanks for the draft. Best, É. -- Hans Havermann gladhobo@teksavvy.com via list.seqfan.eu Thu, Dec 5, 2013, 10:21 AM to Sequence If I understand the change correctly, I think the third term would become 15 (from 16) and the fourth, 25 (from 26). -- M. F. Hasler oeis@hasler.fr via list.seqfan.eu Dec 5, 2013, 10:38 AM to Sequence On Thu, Dec 5, 2013 at 11:21 AM, Hans Havermann wrote: > If I understand the change correctly, I think the third term would become 15 (from 16) and the fourth, 25 (from 26). You are right ! See A233185-A233188 for French and German versions. Maximilian -- Claudio Meller claudiomeller@gmail.com via list.seqfan.eu Dec 5, 2013, 3:06 PM to Sequence In Spanish: 6 4 SEIS 10 8 DIEZ 15 14 QUINCE 26 24 VEINTISEIS 38 36 TREINTA Y OCHO 50 45 CINCUENTA 60 52 SESENTA 66 64 SESENTA Y SEIS 78 76 SETENTA Y OCHO 90 83 NOVENTA 96 95 NOVENTA Y SEIS 100 99 CIEN 110 109 CIENTO DIEZ 126 125 CIENTO VEINTISÉIS 140 139 CIENTO CUARENTA 160 152 CIENTO SESENTA 170 165 CIENTO SETENTA 180 178 CIENTO OCHENTA 198 196 CIENTO NOVENTA Y OCHO 211 210 DOSCIENTOS ONCE 230 227 DOSCIENTOS TREINTA 250 246 DOSCIENTOS CINCUENTA 270 263 DOSCIENTOS SETENTA 286 285 DOSCIENTOS OCHENTA Y SEIS 300 296 TRESCIENTOS 312 311 TRESCIENTOS DOCE 330 329 TRESCIENTOS TREINTA 350 349 TRESCIENTOS CINCUENTA 370 367 TRESCIENTOS SETENTA -- Claudio Meller http://grageasdefarmacia.blogspot.com http://todoanagramas.blogspot.com/ http://simplementenumeros.blogspot.com/ --